Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
8
2
2017
12
01
Existence of common best proximity points of generalized $S$-proximal contractions
1
8
EN
Hemant
Nashine
0000-0002-0250-9172
Department of Mathematics, Texas A \& M University-Kingsville-78363-8202, Texas, USA
drhknashine@gmail.com
Zoran
Kadelburg
University of Belgrade, Faculty of Mathematics, Studentski trg 16, 11000 Beograd, Serbia
kadelbur@matf.bg.ac.rs
10.22075/ijnaa.2017.859.1153
In this article, we introduce a new notion of proximal contraction, named as generalized S-proximal contraction and derive a common best proximity point theorem for proximally commuting non-self mappings, thereby yielding the common optimal approximate solution of some fixed point equations when there is no common solution. We furnish illustrative examples to highlight our results. We extend some results existing in the literature.
common best proximity point,optimal approximate solution,proximally commuting mappings
https://ijnaa.semnan.ac.ir/article_2764.html
https://ijnaa.semnan.ac.ir/article_2764_4a0f5785686f6c06e1cccf3bf040f1c4.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
8
2
2017
12
07
On the natural stabilization of convection diffusion problems using LPIM meshless method
9
22
EN
Ali
Arefmanesh
Department of Mechanical Engineering, University of Kashan, Kashan, Iran
arefmanesh@kashanu.ac.ir
Mahmoud
Abbaszadeh
School of Engineering, University of Warwick, Coventry, United Kingdom
m.abbaszadeh@warwick.ac.uk
10.22075/ijnaa.2016.466
By using the finite element $p$-Version in convection-diffusion problems, we can attain to a stabilized and accurate results. Furthermore, the fundamental of the finite element $p$-Version is augmentation degrees of freedom. Based on the fact that the finite element and the meshless methods have similar concept, it is obvious that many ideas in the finite element can be easily used in the meshless methods. Hence, in this study, the concept of the finite element $p$-Version is applied in the LPIM meshfree method. The results prove that increasing degrees of freedom limits artificial numerical oscillations occurred in very large Peclet numbers.
convection-diffusion problems,LPIM meshless method,natural stabilization,$p$-Version finite element method
https://ijnaa.semnan.ac.ir/article_466.html
https://ijnaa.semnan.ac.ir/article_466_bbb3a1fc16ee7db611610410e3835c9f.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
8
2
2017
12
03
Contractive gauge functions in strongly orthogonal metric spaces
23
28
EN
Maryam
Ramezani
Department of Mathematics, Faculty of Mathematics, University of Bojnord, Bojnord, Iran
mar.ram.math@gmail.com
Hamid
Baghani
Department of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, P.O. Box 98135-674, Zahedan, Iran
h.baghani@gmail.com
10.22075/ijnaa.2016.452
Existence of fixed point in orthogonal metric spaces has been initiated recently by Eshaghi and et al. [On orthogonal sets and Banach fixed Point theorem, Fixed Point Theory, in press]. In this paper, we introduce the notion of the strongly orthogonal sets and prove a genuine generalization of Banach' fixed point theorem and Walter's theorem. Also, we give an example showing that our main theorem is a real generalization of these fixed point theorems.
strongly orthogonal set,Fixed point,gauge function
https://ijnaa.semnan.ac.ir/article_452.html
https://ijnaa.semnan.ac.ir/article_452_2a1a25491ed3b19576dc43dcff80d39b.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
8
2
2017
12
04
Perfect $2$-colorings of the Platonic graphs
29
35
EN
Mohammad Hadi
Alaeiyan
School of Computer Engineering, Iran University of Science and Technology, Narmak, Tehran 16846, Iran
hadi_alaeiyan@comp.iust.ac.ir
Hamed
Karami
School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846, Iran
h_karami@iust.ac.ir
10.22075/ijnaa.2016.455
In this paper, we enumerate the parameter matrices of all perfect $2$-colorings of the Platonic graphs consisting of the tetrahedral graph, the cubical graph, the octahedral graph, the dodecahedral graph, and the icosahedral graph.
Perfect Coloring,Equitable Partition,Platonic Graph
https://ijnaa.semnan.ac.ir/article_455.html
https://ijnaa.semnan.ac.ir/article_455_b232654319dc2a0cb031bc04091ece3d.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
8
2
2017
12
01
Nonstandard explicit third-order Runge-Kutta method with positivity property
37
46
EN
Mohammad
Mehdizadeh Khalsaraei
Department of Mathematics, Faculty of Science, University of Maragheh, 55181-83111 Maragheh, Iran
muhammad.mehdizadeh@gmail.com
10.22075/ijnaa.2016.480
When one solves differential equations, modeling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. Based on general theory for positivity, with an explicit third-order Runge-Kutta method (we will refer to it as RK3 method) positivity is not ensured when applied to the inhomogeneous linear systems and the same result is regained on nonlinear positivity for this method. Here we mean by positivity that the nonnegativity of the components of the initial vector is preserved. Nonstandard finite differences (NSFDs) schemes can improve the accuracy and reduce computational costs of traditional finite difference schemes. In addition to NSFDs produce numerical solutions which also exhibit essential properties of solution. In this paper, we investigate the positivity property for nonstandard RK3 method when applied to the numerical solution of special nonlinear initial value problems (IVPs) for ordinary differential equations (ODEs). We obtain new results for positivity which are important in practical applications. We provide some numerical examples to illustrate our results.
Positivity,Initial value problems,Advection equation,Bergers' equation,Runge-Kutta methods
https://ijnaa.semnan.ac.ir/article_480.html
https://ijnaa.semnan.ac.ir/article_480_bfe54710147d214731391df012a6a25a.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
8
2
2017
12
01
Curvature collineations on Lie algebroid structure
47
63
EN
Esa
Sharahi
Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran
esasharahi@gmail.com
Esmaeil
Peyghan
Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran
epeyghan@gmail.com
Constantin
Arcus
Secondary School "Cornelius Radu", Radinesti Village, 217196 Gorj County, Romania
c_arcus@radinesti.ro
10.22075/ijnaa.2016.516
Considering prolongation of a Lie algebroid equipped with a spray, defining some classical tensors, we show that a Lie symmetry of a spray is a curvature collineation for these tensors.
Curvature collineation,Lie algebroid,Lie symmetry,projectable section,spray
https://ijnaa.semnan.ac.ir/article_516.html
https://ijnaa.semnan.ac.ir/article_516_59906f46ca9f8631db7aac16657b95ac.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
8
2
2017
12
06
On the stability of linear differential equations of second order
65
70
EN
Abbas
Najati
Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran
a.nejati@yahoo.com
Mohammad
Abdollahpour
Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran
mrabdollahpour@yahoo.com
Choonkil
Park
Department of Mathematics, Hanyang University, Seoul, 133--791, South Korea
baak@hanyang.ac.kr
10.22075/ijnaa.2017.1078.1226
The aim of this paper is to investigate the Hyers-Ulam stability of the linear differential equation<br />$$y''(x)+alpha y'(x)+beta y(x)=f(x)$$<br />in general case, where $yin C^2[a,b],$ $fin C[a,b]$ and $-infty<a<b<+infty$. The result of this paper improves a result of Li and Shen [textit{Hyers-Ulam stability of linear differential equations of second order,} Appl. Math. Lett. 23 (2010) 306--309].
Hyers-Ulam stability,linear differential equation of second order
https://ijnaa.semnan.ac.ir/article_2768.html
https://ijnaa.semnan.ac.ir/article_2768_c56749cc1ab49441e4b381aa39b132e9.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
8
2
2017
12
01
Soft double fuzzy semi-topogenous structures
71
88
EN
A.
Ghareeb
Department of Mathematics, Colleges of Science, Al-Baha University, Al-Baha, Saudi Arabia
Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt
a.ghareeb@sci.svu.edu.eg
O.H.
Khalil
Department of Mathematics, College of Science in Al-Zulfi, Majmaah University, Al-Zulfi, Saudi Arabia
Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt
nasserfuzt@hotmail.com
10.22075/ijnaa.2017.1787.1469
The purpose of this paper is to introduce the concept of soft double fuzzy semi-topogenous order. Firstly, we give the definition of soft double fuzzy semi-topogenous order. Secondly, we induce a soft double fuzzy topology from a given soft double fuzzy semi-topogenous order by using soft double fuzzy interior operator.
soft double fuzzy topology,soft double fuzzy interior operator,soft double fuzzy semi-topogenous structure
https://ijnaa.semnan.ac.ir/article_2788.html
https://ijnaa.semnan.ac.ir/article_2788_42478fba2bdf9494bd980f7308e1f221.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
8
2
2017
12
01
Interpolation of fuzzy data by using flat end fuzzy splines
89
97
EN
Reza
Ezzati
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
ezati@kiau.ac.ir
Saeid
Abbasbandy
Department of Applied Mathematics, Imam Khomeini International University, Qazvin, Iran
abbasbandy@yahoo.com
Hossein
Behforooz
Department of Mathematics, Utica College, Utica, New York, 13502, USA
hbehforooz@utica.edu
10.22075/ijnaa.2017.1419.1363
In this paper, a new set of spline functions called ``Flat End Fuzzy Spline" is defined to interpolate given fuzzy data. Some important theorems on these splines together with their existence and uniqueness properties are discussed. Then numerical examples are presented to illustrate the differences between of using our spline and other interpolations that have been studied before.
fuzzy interpolation,extension principle,fuzzy splines
https://ijnaa.semnan.ac.ir/article_2765.html
https://ijnaa.semnan.ac.ir/article_2765_d76b656bd725808a80f0451c76bd26b8.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
8
2
2017
12
01
Translation invariant mappings on KPC-hypergroups
99
107
EN
Seyyed Mohammad
Tabatabaie
null
Department of Mathematics, University of Qom, Qom, Iran
sm.tabatabaie@qom.ac.ir
Faranak
Haghighifar
Department of Mathematics, University of Qom, Qom, Iran
f.haghighifar@yahoo.com
10.22075/ijnaa.2017.1365.1340
In this paper, we give an extension of the Wendel's theorem on KPC-hypergroups. We also show that every translation invariant mapping is corresponding with a unique positive measure on the KPC-hypergroup.
DJS-hypergroup,KPC-hypergroup,Translation Invariant Mapping,Wendel's Theorem
https://ijnaa.semnan.ac.ir/article_2785.html
https://ijnaa.semnan.ac.ir/article_2785_050eaa7a4eae270a339a107852a64608.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
8
2
2017
12
01
Some new Ostrowski type fractional integral inequalities for generalized $(r;g,s,m,varphi)$-preinvex functions via Caputo $k$-fractional derivatives
109
124
EN
Artion
Kashuri
Department of Mathematics, Faculty of Technical Science, University "Ismail Qemali", 9400, Vlora, Albania
artionkashuri@gmail.com
Rozana
Liko
Department of Mathematics, Faculty of Technical Science, University "Ismail Qemali", 9400, Vlora, Albania
rozanaliko86@gmail.com
10.22075/ijnaa.2017.11722.1585
In the present paper, the notion of generalized $(r;g,s,m,varphi)$-preinvex function is applied to establish some new generalizations of Ostrowski type integral inequalities via Caputo $k$-fractional derivatives. At the end, some applications to special means are given.
Ostrowski type inequality,H"{o}lder's inequality,Minkowski's inequality,$s$-convex function in the second sense,$m$-invex
https://ijnaa.semnan.ac.ir/article_2790.html
https://ijnaa.semnan.ac.ir/article_2790_0b41c4fb5b26b287e9fc35c76b4ec926.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
8
2
2017
12
01
Mathematical modeling of optimized SIRS epidemic model and some dynamical behavior of the solution
125
134
EN
Mehdi
Nadjafikhah
Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, Iran
m_nadjafikhah@iust.ac.ir
Saeid
Shagholi
Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, Iran
sshagholi@mathdep.iust.ac.ir
10.22075/ijnaa.2017.11821.1592
In this paper, a generalized mathematical model of spread of infectious disease as SIRS epidemic model is considered as a nonlinear system of differential equation. We prove that for positive initial conditions the resulting equivalence system has positive solution and under some hypothesis, this system with initial positive condition, has a positive $T$-periodic solution which is globally asymptotically stable. For numerical simulations the fourth order Runge-Kutta method is applied to the nonlinear system of differential equations.
Mathematical modeling,epidemic SIRS model,positive solution,globally asymptotically stability
https://ijnaa.semnan.ac.ir/article_2792.html
https://ijnaa.semnan.ac.ir/article_2792_035182d58bb9842edde0597201b211da.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
8
2
2017
12
01
Modified degenerate Carlitz's $q$-bernoulli polynomials and numbers with weight ($alpha ,beta $)
135
144
EN
Ugur
Duran
0000-0002-5717-1199
Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, Gaziantep, 27310, Turkey
mtdrnugur@gmail.com
Mehmet
Acikgoz
Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, Gaziantep, 27310, Turkey
acikgoz@gantep.edu.tr
10.22075/ijnaa.2017.11767.1588
The main goal of the present paper is to construct some families of the Carlitz's $q$-Bernoulli polynomials and numbers. We firstly introduce the modified Carlitz's $q$-Bernoulli polynomials and numbers with weight ($_{p}$. We then define the modified degenerate Carlitz's $q$-Bernoulli polynomials and numbers with weight ($alpha ,beta $) and obtain some recurrence relations and other identities. Moreover, we derive some correlations with the modified Carlitz's $q$-Bernoulli polynomials with weight ($alpha ,beta $), the modified degenerate Carlitz's $q$-Bernoulli polynomials with weight ($alpha ,beta $), the Stirling numbers of the first kind and second kind.
Carlitz's $q$-Bernoulli polynomials,Stirling numbers of the first kind,Stirling numbers of the second kind,$p$-adic $q$-integral
https://ijnaa.semnan.ac.ir/article_2791.html
https://ijnaa.semnan.ac.ir/article_2791_48a0eba5d8560ea93b810f1b3562b4eb.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
8
2
2017
12
01
Coupled coincidence point and common coupled fixed point theorems in complex valued metric spaces
145
158
EN
Fayyaz
Rouzkard
Farhangian University, Shariati Pardis, Sari, Mazandaran Iran
fayyazrouzkard@gmail.com
Mohammad
Imdad
Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India
mhimdad@yahoo.co.in
10.22075/ijnaa.2017.521
In this paper, we introduce the concept of a w-compatible mappings and utilize the same to discuss the ideas of coupled coincidence point and coupled point of coincidence for nonlinear contractive mappings in the context of complex valued metric spaces besides proving existence theorems which are following by corresponding unique coupled common fixed point theorems for such mappings. Some illustrative examples are also given to substantiate our newly proved results.
Common fixed point,Contractive type mapping,coupled coincidence point,coupled point of coincidence,Complex valued metric space
https://ijnaa.semnan.ac.ir/article_521.html
https://ijnaa.semnan.ac.ir/article_521_2a61f222299a2c5adf3e26b8819aaa3a.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
8
2
2017
12
01
Global attractor for a nonlocal hyperbolic problem on ${mathcal{R}}^{N}$
159
168
EN
Perikles
Papadopoulos
Department of Electronics Engineering, School of Technological Applications, Piraeus University of Applied Sciences (Technological Education Institute of Piraeus), GR 11244, Egaleo, Athens, Greece
ppapadop@puas.gr
N.L.
Matiadou
Department of Electronics Engineering, School of Technological Applications, Piraeus University of Applied Sciences (Technological Education Institute of Piraeus), GR 11244, Egaleo, Athens, Greece
lmatiadou@yahoo.gr
10.22075/ijnaa.2017.11600.1575
We consider the quasilinear Kirchhoff's problem<br />$$ u_{tt}-phi (x)||nabla u(t)||^{2}Delta u+f(u)=0 ,;; x in {mathcal{R}}^{N}, ;; t geq 0,$$<br />with the initial conditions $ u(x,0) = u_0 (x)$ and $u_t(x,0) = u_1 (x)$, in the case where $N geq 3, ; f(u)=|u|^{a}u$ and $(phi (x))^{-1} in L^{N/2}({mathcal{R}}^{N})cap L^{infty}({mathcal{R}}^{N} )$ is a positive function. The purpose of our work is to study the long time behaviour of the solution of this equation. Here, we prove the existence of a global attractor for this equation in the strong topology of the space ${cal X}_{1}=:{cal D}^{1,2}({mathcal{R}}^{N}) times L^{2}_{g}({mathcal{R}}^{N}).$ We succeed to extend some of our earlier results concerning the asymptotic behaviour of the solution of the problem.
quasilinear hyperbolic equations,Kirchhoff strings,global attractor,generalised Sobolev spaces,weighted $L^p$ Spaces
https://ijnaa.semnan.ac.ir/article_2793.html
https://ijnaa.semnan.ac.ir/article_2793_ef30a57e5aaa4eb687c61b37a80ea4d1.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
8
2
2017
12
01
Computational method based on triangular operational matrices for solving nonlinear stochastic differential equations
169
179
EN
Mahnaz
Asgari
Department of Engineering,~Abhar Branch,~Islamic Azad University, Abhar, Iran
mah_sgr@yahoo.com
Morteza
khodabin
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
m-khodabin@kiau.ac.ir
10.22075/ijnaa.2017.1023.1198
In this article, a new numerical method based on triangular functions for solving nonlinear stochastic differential equations is presented. For this, the stochastic operational matrix of triangular functions for It^{o} integral are determined. Computation of presented method is very simple and attractive. In addition, convergence analysis and numerical examples that illustrate accuracy and efficiency of the method are presented.
Brownian motion,It^{o} integral,Nonlinear stochastic differential equation,Stochastic operational matrix,Triangular function
https://ijnaa.semnan.ac.ir/article_2783.html
https://ijnaa.semnan.ac.ir/article_2783_c6fbfe31fd6236b020f1a1ec4c88ae52.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
8
2
2017
12
01
On the approximation by Chlodowsky type generalization of (p,q)-Bernstein operators
181
200
EN
Khursheed
J.
Ansari
Department of Mathematics, College of Science, King Khalid University, 61413,
Abha, Saudi Arabia
ansari.jkhursheed@gmail.com
Ali
Karaisa
Department of Mathematics-Computer Sciences, Faculty of Sciences, Necmettin
Erbakan University Meram Campus, 42090 Meran, Konya, Turkey
akaraisa@konya.edu.tr
10.22075/ijnaa.2017.1827.1479
In the present article, we introduce Chlodowsky variant of $(p,q)$-Bernstein operators and compute the moments for these operators which are used in proving our main results. Further, we study some approximation properties of these new operators, which include the rate of convergence using usual modulus of continuity and also the rate of convergence when the function $f$ belongs to the class Lip$_{M}(alpha )$. Moreover, we also discuss convergence and rate of approximation in weighted spaces and weighted statistical approximation properties of the sequence of positive linear operators defined by us.
$(p,q)$-integers,Bernstein operators,positive linear operators,Korovkin type approximation theorem,statistical approximation
https://ijnaa.semnan.ac.ir/article_2789.html
https://ijnaa.semnan.ac.ir/article_2789_8c00a08033e702b77e6d822b3272f202.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
8
2
2017
12
01
A necessary condition for multiple objective fractional programming
201
207
EN
Rezvan
Kamali
Department of Mathematics, Faculty of Science, University of Isfahan, Isfahan, Iran
reka_math@yahoo.com
Ali
Davari
Department of Mathematics, Khansar Faculty of Mathematics and Computer Science, Khansar, Iran
a_davari2002@yahoo.com
10.22075/ijnaa.2016.482
In this paper, we establish a proof for a necessary condition for multiple objective fractional programming. In order to derive the set of necessary conditions, we employ an equivalent parametric problem. Also, we present the related semi parametric model.
Multiple objective fractional programming,Generalized n-set convex function,Efficient solution
https://ijnaa.semnan.ac.ir/article_482.html
https://ijnaa.semnan.ac.ir/article_482_73a53fecfb7bfc8a6778a60cabed4272.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
8
2
2017
12
01
On generalized Hermite-Hadamard inequality for generalized convex function
209
222
EN
Mehmet Zeki
Sarikaya
Department of Mathematics, Faculty of Science and Arts, D\"{u}zce University, D\"{u}zce-Turkey
sarikayamz@gmail.com
Huseyin
Budak
Department of Mathematics, Faculty of Science and Arts, D\"{u}zce University, D\"{u}zce-Turkey
hsyn.budak@gmail.com
10.22075/ijnaa.2017.11313.1552
In this paper, a new inequality for generalized convex functions which is related to the left side of generalized Hermite-Hadamard type inequality is obtained. Some applications for some generalized special means are also given.
Generalized Hermite-Hadamard inequality,Generalized H"{o}lder inequality,Generalized convex functions
https://ijnaa.semnan.ac.ir/article_2797.html
https://ijnaa.semnan.ac.ir/article_2797_fe30c34bcf477187700e2c4e5c003604.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
8
2
2017
12
20
Analytical aspects of the interval unilateral quadratic matrix equations and their united solution sets
223
241
EN
Tayyebe
Haqiri
School of Mathematics and Computer Science, Damghan University, Damghan, Iran;
Member of Young Researchers Society of Shahid Bahonar University of Kerman, Kerman, P.O. Box 76169-14111, Iran
thaqiri@gmail.com
Azim
Rivaz
Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
arivaz@uk.ac.ir
Mahmoud
Mohseni Moghadam
Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
mohseni@uk.ac.ir
10.22075/ijnaa.2017.10778.1523
This paper introduces the emph{interval unilateral quadratic matrix equation}, $IUQe$ and attempts to find various analytical results on its AE-solution sets in which $A,B$ and $CCC$ are known real interval matrices, while $X$ is an unknown matrix. These results are derived from a generalization of some results of Shary. We also give sufficient conditions for non-emptiness of some quasi-solution sets, provided that $A$ is regular. As the most common case, the united solution set has been studied and two direct methods for computing an outer estimation and an inner estimation of the united solution set of an interval unilateral quadratic matrix equation are proposed. The suggested techniques are based on nonlinear programming as well as sensitivity analysis.
AE-solution sets,interval unilateral quadratic matrix equation,united solution set,nonlinear programming,Sensitivity analysis
https://ijnaa.semnan.ac.ir/article_2796.html
https://ijnaa.semnan.ac.ir/article_2796_50bf006dbe46ff6c42b14348865a347c.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
8
2
2017
12
01
On exponential domination and graph operations
243
250
EN
Betul
Atay
Department of Computer and Inst. Tech. Edu., Faculty of Education, Agri Ibrahim Cecen University, Agri, Turkey
btlatay87@gmail.com
Aysun
Aytac
Department of Mathematics, Faculty of Science, Ege University, 35100 Bornova-Izmir, Turkey
aysun.aytac@ege.edu.tr
10.22075/ijnaa.2017.3056.1494
An exponential dominating set of graph $G = (V,E )$ is a subset $Ssubseteq V(G)$ such that $sum_{uin S}(1/2)^{overline{d}{(u,v)-1}}geq 1$ for every vertex $v$ in $V(G)-S$, where $overline{d}(u,v)$ is the distance between vertices $u in S$ and $v in V(G)-S$ in the graph $G -(S-{u})$. The exponential domination number, $gamma_{e}(G)$, is the smallest cardinality of an exponential dominating set. Graph operations are important methods for constructing new graphs, and they play key roles in the design and analysis of networks. In this study, we consider the exponential domination number of graph operations including edge corona, neighborhood corona and power.
Graph vulnerability,network design and communication,exponential domination number,edge corona,neighbourhood corona
https://ijnaa.semnan.ac.ir/article_2767.html
https://ijnaa.semnan.ac.ir/article_2767_30d3be476f5e7e4708605bbc92f6406d.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
8
2
2017
12
22
$(varphi_1, varphi_2)$-variational principle
251
261
EN
Abdelhakim
Maaden
Universit\'e Sultan Moulay Slimane, Facult\'e des Sciences et Techniques, Laboratoire de Math\'ematiques et Applications, B.P. 523, Beni-Mellal 23000, Maroc
hmaaden2002@yahoo.fr
Stouti
Abdelkader
Universit\'e Sultan Moulay Slimane, Facult\'e des Sciences et Techniques, Laboratoire de Math\'ematiques et Applications, B.P. 523, Beni-Mellal 23000, Maroc
stouti@yahoo.com
10.22075/ijnaa.2017.1664.1439
In this paper we prove that if $X $ is a Banach space, then for every lower semi-continuous bounded below function $f, $ there exists a $left(varphi_1, varphi_2right)$-convex function $g, $ with arbitrarily small norm, such that $f + g $ attains its strong minimum on $X. $ This result extends some of the well-known varitional principles as that of Ekeland [On the variational principle, J. Math. Anal. Appl. 47 (1974) 323--353], that of Borwein-Preiss [A smooth variational principle with applications to subdifferentiability and to differentiability of convex functions, Trans. Amer. Math. Soc. 303 (1987) 517--527] and that of Deville-Godefroy-Zizler [Un principe variationel utilisant des fonctions bosses, C. R. Acad. Sci. (Paris). Ser.I 312 (1991) 281--286] and [A smooth variational principle with applications to Hamilton-Jacobi equations in infinite dimensions, J. Funct. Anal. 111 (1993) 197--212].
$left(varphi_1, varphi_2right)$-convex function,$left(varphi_1, varphi_2right)$-variational principle,Ekeland's variational principle,smooth variational principle
https://ijnaa.semnan.ac.ir/article_2766.html
https://ijnaa.semnan.ac.ir/article_2766_da52f80c47f3aee56ce7052c87770f23.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
8
2
2017
12
23
Existence and uniqueness of the solution for a general system of operator equations in $b-$metric spaces endowed with a graph
263
276
EN
Cristian
Chifu
Department of Business, Faculty of Business, Babes-Bolyai University, Cluj-Napoca, Romania
cristian.chifu@tbs.ubbcluj.ro
Gabriela
Petrusel
Department of Business, Faculty of Business, Babes-Bolyai University, Cluj-Napoca, Romania
gabi.petrusel@tbs.ubbcluj.ro
10.22075/ijnaa.2017.11562.1570
The purpose of this paper is to present some coupled fixed point results on a metric space endowed with two $b$-metrics. We shall apply a fixed point theorem for an appropriate operator on the Cartesian product of the given spaces endowed with directed graphs. Data dependence, well-posedness and Ulam-Hyers stability are also studied. The results obtained here will be applied to prove the existence and uniqueness of the solution for a system of integral equations.
Fixed point,Coupled fixed point,$b$-metric space,connected graph,integral equations
https://ijnaa.semnan.ac.ir/article_2800.html
https://ijnaa.semnan.ac.ir/article_2800_62e25ec2b3418aa3f744b6478d9fbcde.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
8
2
2017
12
01
Application of fractional-order Bernoulli functions for solving fractional Riccati differential equation
277
292
EN
Yadollah
Ordokhani
Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran
ordokhani@alzahra.ac.ir
Parisa
Rahimkhani
Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran
National Elites Foundation, Tehran, Iran
p.rahimkhani@alzahra.ac.ir
Esmail
Babolian
Department of Computer Science, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran
babolian@khu.ac.ir
10.22075/ijnaa.2017.1476.1379
In this paper, a new numerical method for solving the fractional Riccati differential equation is presented. The fractional derivatives are described in the Caputo sense. The method is based upon fractional-order Bernoulli functions approximations. First, the fractional-order Bernoulli functions and their properties are presented. Then, an operational matrix of fractional order integration is derived and is utilized to reduce the under study problem to a system of algebraic equations. Error analysis included the residual error estimation and the upper bound of the absolute errors are introduced for this method. The technique and the error analysis are applied to some problems to demonstrate the validity and applicability of our method.
Fractional Riccati differential equation,Fractional-order Bernoulli functions,Caputo derivative,Operational matrix,Collocation method
https://ijnaa.semnan.ac.ir/article_2795.html
https://ijnaa.semnan.ac.ir/article_2795_3990006fa9915eb0af3345e8046f7bc8.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
8
2
2017
12
01
On some fixed points properties and convergence theorems for a Banach operator in hyperbolic spaces
293
306
EN
Akindele Adebayo
Mebawondu
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa
dele@aims.ac.za
Lateef
Jolaoso
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa
216074984@stu.ukzn.ac.za
Hammed
Abass
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa
216075727@stu.ukzn.ac.za
10.22075/ijnaa.2017.11887.1594
In this paper, we prove some fixed points properties and demiclosedness principle for a Banach operator in uniformly convex hyperbolic spaces. We further propose an iterative scheme for approximating a fixed point of a Banach operator and establish some strong and $Delta$-convergence theorems for such operator in the frame work of uniformly convex hyperbolic spaces. The results obtained in this paper extend and generalize corresponding results on uniformly convex Banach spaces, CAT(0) spaces and many other results in this direction.
Banach operator,uniformly convex hyperbolic spaces,strong and $Delta$-convergence theorem,Modified Picard Normal S-iteration
https://ijnaa.semnan.ac.ir/article_2799.html
https://ijnaa.semnan.ac.ir/article_2799_2ea33223c55fba3700f88bd7aefc3695.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
8
2
2017
12
26
Some common fixed point theorems for four $(psi,varphi)$-weakly contractive mappings satisfying rational expressions in ordered partial metric spaces
307
326
EN
Rashwan
Rashwan
Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
rr_rashwan54@yahoo.com
S.M.
Saleh
Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
samirasaleh2007@yahoo.com
10.22075/ijnaa.2016.468
The aim of this paper is to prove some common fixed point theorems for four mappings satisfying $(psi,varphi)$-weak contractions involving rational expressions in ordered partial metric spaces. Our results extend, generalize and improve some well-known results in the literature. Also, we give two examples to illustrate our results.
Common fixed point,rational contractions,ordered partial metric spaces,dominating and dominated mappings
https://ijnaa.semnan.ac.ir/article_468.html
https://ijnaa.semnan.ac.ir/article_468_a5b9c5cc09ff9b3a978f98266a1b155a.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
8
2
2017
12
01
Mazur-Ulam theorem in probabilistic normed groups
327
333
EN
Alireza
Pourmoslemi
Department of Mathematics, Payame Noor University, Tehran, Iran
a_pourmoslemy@pnu.ac.ir
Kourosh
Nourouzi
Faculty of Mathematics, K.N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran
nourouzi@kntu.ac.ir
10.22075/ijnaa.2017.1281.1318
In this paper, we give a probabilistic counterpart of Mazur-Ulam theorem in probabilistic normed groups. We show, under some conditions, that every surjective isometry between two probabilistic normed groups is a homomorphism.
Probabilistic normed groups,Invariant probabilistic metrics,Mazur-Ulam Theorem
https://ijnaa.semnan.ac.ir/article_2786.html
https://ijnaa.semnan.ac.ir/article_2786_313d118769848a5d41636e321e9950d6.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
8
2
2017
12
01
Fixed point theorems for generalized quasi-contractions in cone $b$-metric spaces over Banach algebras without the assumption of normality with applications
335
353
EN
Shaoyuan
Xu
School of Mathematics and Statistics, Hanshan Normal University, Chaozhou, 521041, China
xushaoyuan@126.com
Suyu
Cheng
Library, Hanshan Normal University, Chaozhou, 521041, China
chengsuyu1992@126.com
Suzana
Aleksic
Department of Mathematics and Informatics, Faculty of Science, University of Kragujevac, Radoja Domanovi\'ca 12, 34000 Kragujevac, Serbia
suzanasimic@kg.ac.rs
10.22075/ijnaa.2017.1857.1483
In this paper, we introduce the concept of generalized quasi-contractions in the setting of cone $b$-metric spaces over Banach algebras. By omitting the assumption of normality we establish common fixed point theorems for the generalized quasi-contractions with the spectral radius $r(lambda)$ of the quasi-contractive constant vector $lambda$ satisfying $r(lambda)in [0,frac{1}{s})$ in the setting of cone $b$-metric spaces over Banach algebras, where the coefficient $s$ satisfies $sge 1$. As consequences, we obtain common fixed point theorems for the generalized $g$-quasi-contractions in the setting of such spaces. The main results generalize, extend and unify several well-known comparable results in the literature. Moreover, we apply our main results to some nonlinear equations, which shows that these results are more general than corresponding ones in the setting of $b$-metric or metric spaces.
cone $b$-metric spaces over Banach algebras,non-normal cones,$c$-sequences,generalized quasi-contractions,Fixed point theorem
https://ijnaa.semnan.ac.ir/article_2787.html
https://ijnaa.semnan.ac.ir/article_2787_c82fdf395409faa23840674b2855da21.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
8
2
2017
12
01
L$^q$ inequalities for the ${s^{th}}$ derivative of a polynomial
355
362
EN
Ahmad
Zireh
Department of Mathematics, Shahrood University of Technology, Shahrood, Iran
azireh@gmail.com
10.22075/ijnaa.2017.1286.1321
Let $f(z)$ be an analytic function on the unit disk ${zinmathbb{C}, |z|leq 1}$, for each $q>0$, the $|f|_{q}$ is defined as follows<br />begin{align*}<br />begin{split}<br />&left|fright|_q:=left{frac{1}{2pi}int_0^{2pi}left|f(e^{itheta})right|^qdthetaright}^{1/q},<br /> 0<q<infty,\<br />&left|fright|_{infty}:=max_{|z|=1}left|f(z)right|.<br />end{split}<br />end{align*}<br /> Govil and Rahman [{it Functions of exponential type not vanishing in a half-plane and related polynomials}, { Trans. Amer. Math. Soc.} {137} (1969) 501--517] proved that if $p(z)$ is a polynomial of degree $n$, which does not vanish in $|z|<k$, where $kgeq 1$, then for each $q>0$,<br />begin{align*}<br />left|p'right|_{q}leq frac{n}{|k+z|_q}|p|_{q}.<br />end{align*}<br />In this paper, we shall present an interesting generalization and refinement of this result which include some previous results.
Derivative,Polynomial,$L^q$ Inequality,Maximum modulus,Restricted Zeros
https://ijnaa.semnan.ac.ir/article_2801.html
https://ijnaa.semnan.ac.ir/article_2801_1533fb6d1e1801bc30789ab8dc04255b.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
8
2
2017
12
01
Dynamics of higher order rational difference equation $x_{n+1}=(alpha+beta x_{n})/(A + Bx_{n}+ Cx_{n-k})$
363
379
EN
Abu Alhalawa
Muna
Department of Mathematics, Faculty of Science, Birzeit University, Palestine
mabualhalawa@birzeit.edu
Mohammad
Saleh
Department of Mathematics, Faculty of Science, Birzeit University, Palestine
msaleh@birzeit.edu
10.22075/ijnaa.2017.10822.1526
The main goal of this paper is to investigate the periodic character, invariant intervals, oscillation and global stability and other new results of all positive solutions of the equation<br />$$x_{n+1}=frac{alpha+beta x_{n}}{A + Bx_{n}+ Cx_{n-k}},~~ n=0,1,2,ldots,$$<br />where the parameters $alpha$, $beta$, $A$, $B$ and $C$ are positive, and the initial conditions $x_{-k},x_{-k+1},ldots,x_{-1},x_{0}$ are positive real numbers and $kin{1,2,3,ldots}$. We give a detailed description of the semi-cycles of solutions and determine conditions under which the equilibrium points are globally asymptotically stable. In particular, our paper is a generalization of the rational difference equation that was investigated by Kulenovic et al. [The Dynamics of $x_{n+1}=frac{alpha +beta x_{n}}{A+Bx_{n}+ C x_{n-1}}$, Facts and Conjectures, Comput. Math. Appl. 45 (2003) 1087--1099].
stability theory,semi-cycle analysis,invariant intervals,nonlinear difference equations,discrete dynamical systems
https://ijnaa.semnan.ac.ir/article_2794.html
https://ijnaa.semnan.ac.ir/article_2794_5faa22d45bfb19c931f7a566b1d51774.pdf