eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2017-12-01
8
2
1
8
10.22075/ijnaa.2017.859.1153
2764
Existence of common best proximity points of generalized $S$-proximal contractions
Hemant Nashine
drhknashine@gmail.com
1
Zoran Kadelburg
kadelbur@matf.bg.ac.rs
2
Department of Mathematics, Texas A \& M University-Kingsville-78363-8202, Texas, USA
University of Belgrade, Faculty of Mathematics, Studentski trg 16, 11000 Beograd, Serbia
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.
https://ijnaa.semnan.ac.ir/article_2764_4a0f5785686f6c06e1cccf3bf040f1c4.pdf
common best proximity point
optimal approximate solution
proximally commuting mappings
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2017-12-07
8
2
9
22
10.22075/ijnaa.2016.466
466
On the natural stabilization of convection diffusion problems using LPIM meshless method
Ali Arefmanesh
arefmanesh@kashanu.ac.ir
1
Mahmoud Abbaszadeh
m.abbaszadeh@warwick.ac.uk
2
Department of Mechanical Engineering, University of Kashan, Kashan, Iran
School of Engineering, University of Warwick, Coventry, United Kingdom
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.
https://ijnaa.semnan.ac.ir/article_466_bbb3a1fc16ee7db611610410e3835c9f.pdf
convection-diffusion problems
LPIM meshless method
natural stabilization
$p$-Version finite element method
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2017-12-03
8
2
23
28
10.22075/ijnaa.2016.452
452
Contractive gauge functions in strongly orthogonal metric spaces
Maryam Ramezani
mar.ram.math@gmail.com
1
Hamid Baghani
h.baghani@gmail.com
2
Department of Mathematics, Faculty of Mathematics, University of Bojnord, Bojnord, Iran
Department of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, P.O. Box 98135-674, Zahedan, Iran
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.
https://ijnaa.semnan.ac.ir/article_452_2a1a25491ed3b19576dc43dcff80d39b.pdf
strongly orthogonal set
Fixed point
gauge function
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2017-12-04
8
2
29
35
10.22075/ijnaa.2016.455
455
Perfect $2$-colorings of the Platonic graphs
Mohammad Hadi Alaeiyan
hadi_alaeiyan@comp.iust.ac.ir
1
Hamed Karami
h_karami@iust.ac.ir
2
School of Computer Engineering, Iran University of Science and Technology, Narmak, Tehran 16846, Iran
School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846, Iran
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.
https://ijnaa.semnan.ac.ir/article_455_b232654319dc2a0cb031bc04091ece3d.pdf
Perfect Coloring
Equitable Partition
Platonic Graph
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2017-12-01
8
2
37
46
10.22075/ijnaa.2016.480
480
Nonstandard explicit third-order Runge-Kutta method with positivity property
Mohammad Mehdizadeh Khalsaraei
muhammad.mehdizadeh@gmail.com
1
Department of Mathematics, Faculty of Science, University of Maragheh, 55181-83111 Maragheh, Iran
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.
https://ijnaa.semnan.ac.ir/article_480_bfe54710147d214731391df012a6a25a.pdf
Positivity
Initial value problems
Advection equation
Bergers' equation
Runge-Kutta methods
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2017-12-01
8
2
47
63
10.22075/ijnaa.2016.516
516
Curvature collineations on Lie algebroid structure
Esa Sharahi
esasharahi@gmail.com
1
Esmaeil Peyghan
epeyghan@gmail.com
2
Constantin Arcus
c_arcus@radinesti.ro
3
Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran
Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran
Secondary School "Cornelius Radu", Radinesti Village, 217196 Gorj County, Romania
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.
https://ijnaa.semnan.ac.ir/article_516_59906f46ca9f8631db7aac16657b95ac.pdf
Curvature collineation
Lie algebroid
Lie symmetry
projectable section
spray
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2017-12-06
8
2
65
70
10.22075/ijnaa.2017.1078.1226
2768
On the stability of linear differential equations of second order
Abbas Najati
a.nejati@yahoo.com
1
Mohammad Abdollahpour
mrabdollahpour@yahoo.com
2
Choonkil Park
baak@hanyang.ac.kr
3
Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran
Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran
Department of Mathematics, Hanyang University, Seoul, 133--791, South Korea
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].
https://ijnaa.semnan.ac.ir/article_2768_c56749cc1ab49441e4b381aa39b132e9.pdf
Hyers-Ulam stability
linear differential equation of second order
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2017-12-01
8
2
71
88
10.22075/ijnaa.2017.1787.1469
2788
Soft double fuzzy semi-topogenous structures
A. Ghareeb
a.ghareeb@sci.svu.edu.eg
1
O.H. Khalil
nasserfuzt@hotmail.com
2
Department of Mathematics, Colleges of Science, Al-Baha University, Al-Baha, Saudi Arabia Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt
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
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.
https://ijnaa.semnan.ac.ir/article_2788_42478fba2bdf9494bd980f7308e1f221.pdf
soft double fuzzy topology
soft double fuzzy interior operator
soft double fuzzy semi-topogenous structure
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2017-12-01
8
2
89
97
10.22075/ijnaa.2017.1419.1363
2765
Interpolation of fuzzy data by using flat end fuzzy splines
Reza Ezzati
ezati@kiau.ac.ir
1
Saeid Abbasbandy
abbasbandy@yahoo.com
2
Hossein Behforooz
hbehforooz@utica.edu
3
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
Department of Applied Mathematics, Imam Khomeini International University, Qazvin, Iran
Department of Mathematics, Utica College, Utica, New York, 13502, USA
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.
https://ijnaa.semnan.ac.ir/article_2765_d76b656bd725808a80f0451c76bd26b8.pdf
fuzzy interpolation
extension principle
fuzzy splines
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2017-12-01
8
2
99
107
10.22075/ijnaa.2017.1365.1340
2785
Translation invariant mappings on KPC-hypergroups
Seyyed Mohammad Tabatabaie
sm.tabatabaie@qom.ac.ir
1
Faranak Haghighifar
f.haghighifar@yahoo.com
2
Department of Mathematics, University of Qom, Qom, Iran
Department of Mathematics, University of Qom, Qom, Iran
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.
https://ijnaa.semnan.ac.ir/article_2785_050eaa7a4eae270a339a107852a64608.pdf
DJS-hypergroup
KPC-hypergroup
Translation Invariant Mapping
Wendel's Theorem
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2017-12-01
8
2
109
124
10.22075/ijnaa.2017.11722.1585
2790
Some new Ostrowski type fractional integral inequalities for generalized $(r;g,s,m,varphi)$-preinvex functions via Caputo $k$-fractional derivatives
Artion Kashuri
artionkashuri@gmail.com
1
Rozana Liko
rozanaliko86@gmail.com
2
Department of Mathematics, Faculty of Technical Science, University "Ismail Qemali", 9400, Vlora, Albania
Department of Mathematics, Faculty of Technical Science, University "Ismail Qemali", 9400, Vlora, Albania
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.
https://ijnaa.semnan.ac.ir/article_2790_0b41c4fb5b26b287e9fc35c76b4ec926.pdf
Ostrowski type inequality
H"{o}lder's inequality
Minkowski's inequality
$s$-convex function in the second sense
$m$-invex
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2017-12-01
8
2
125
134
10.22075/ijnaa.2017.11821.1592
2792
Mathematical modeling of optimized SIRS epidemic model and some dynamical behavior of the solution
Mehdi Nadjafikhah
m_nadjafikhah@iust.ac.ir
1
Saeid Shagholi
sshagholi@mathdep.iust.ac.ir
2
Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, Iran
Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, Iran
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.
https://ijnaa.semnan.ac.ir/article_2792_035182d58bb9842edde0597201b211da.pdf
Mathematical modeling
epidemic SIRS model
positive solution
globally asymptotically stability
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2017-12-01
8
2
135
144
10.22075/ijnaa.2017.11767.1588
2791
Modified degenerate Carlitz's $q$-bernoulli polynomials and numbers with weight ($alpha ,beta $)
Ugur Duran
mtdrnugur@gmail.com
1
Mehmet Acikgoz
acikgoz@gantep.edu.tr
2
Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, Gaziantep, 27310, Turkey
Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, Gaziantep, 27310, Turkey
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.
https://ijnaa.semnan.ac.ir/article_2791_48a0eba5d8560ea93b810f1b3562b4eb.pdf
Carlitz's $q$-Bernoulli polynomials
Stirling numbers of the first kind
Stirling numbers of the second kind
$p$-adic $q$-integral
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2017-12-01
8
2
145
158
10.22075/ijnaa.2017.521
521
Coupled coincidence point and common coupled fixed point theorems in complex valued metric spaces
Fayyaz Rouzkard
fayyazrouzkard@gmail.com
1
Mohammad Imdad
mhimdad@yahoo.co.in
2
Farhangian University, Shariati Pardis, Sari, Mazandaran Iran
Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India
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.
https://ijnaa.semnan.ac.ir/article_521_2a61f222299a2c5adf3e26b8819aaa3a.pdf
Common fixed point
Contractive type mapping
coupled coincidence point
coupled point of coincidence
Complex valued metric space
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2017-12-01
8
2
159
168
10.22075/ijnaa.2017.11600.1575
2793
Global attractor for a nonlocal hyperbolic problem on ${mathcal{R}}^{N}$
Perikles Papadopoulos
ppapadop@puas.gr
1
N.L. Matiadou
lmatiadou@yahoo.gr
2
Department of Electronics Engineering, School of Technological Applications, Piraeus University of Applied Sciences (Technological Education Institute of Piraeus), GR 11244, Egaleo, Athens, Greece
Department of Electronics Engineering, School of Technological Applications, Piraeus University of Applied Sciences (Technological Education Institute of Piraeus), GR 11244, Egaleo, Athens, Greece
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.
https://ijnaa.semnan.ac.ir/article_2793_ef30a57e5aaa4eb687c61b37a80ea4d1.pdf
quasilinear hyperbolic equations
Kirchhoff strings
global attractor
generalised Sobolev spaces
weighted $L^p$ Spaces
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2017-12-01
8
2
169
179
10.22075/ijnaa.2017.1023.1198
2783
Computational method based on triangular operational matrices for solving nonlinear stochastic differential equations
Mahnaz Asgari
mah_sgr@yahoo.com
1
Morteza khodabin
m-khodabin@kiau.ac.ir
2
Department of Engineering,~Abhar Branch,~Islamic Azad University, Abhar, Iran
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
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.
https://ijnaa.semnan.ac.ir/article_2783_c6fbfe31fd6236b020f1a1ec4c88ae52.pdf
Brownian motion
It^{o} integral
Nonlinear stochastic differential equation
Stochastic operational matrix
Triangular function
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2017-12-01
8
2
181
200
10.22075/ijnaa.2017.1827.1479
2789
On the approximation by Chlodowsky type generalization of (p,q)-Bernstein operators
Khursheed Ansari
ansari.jkhursheed@gmail.com
1
Ali Karaisa
akaraisa@konya.edu.tr
2
Department of Mathematics, College of Science, King Khalid University, 61413,
Abha, Saudi Arabia
Department of Mathematics-Computer Sciences, Faculty of Sciences, Necmettin Erbakan University Meram Campus, 42090 Meran, Konya, Turkey
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.
https://ijnaa.semnan.ac.ir/article_2789_8c00a08033e702b77e6d822b3272f202.pdf
$(p,q)$-integers
Bernstein operators
positive linear operators
Korovkin type approximation theorem
statistical approximation
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2017-12-01
8
2
201
207
10.22075/ijnaa.2016.482
482
A necessary condition for multiple objective fractional programming
Rezvan Kamali
reka_math@yahoo.com
1
Ali Davari
a_davari2002@yahoo.com
2
Department of Mathematics, Faculty of Science, University of Isfahan, Isfahan, Iran
Department of Mathematics, Khansar Faculty of Mathematics and Computer Science, Khansar, Iran
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.
https://ijnaa.semnan.ac.ir/article_482_73a53fecfb7bfc8a6778a60cabed4272.pdf
Multiple objective fractional programming
Generalized n-set convex function
Efficient solution
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2017-12-01
8
2
209
222
10.22075/ijnaa.2017.11313.1552
2797
On generalized Hermite-Hadamard inequality for generalized convex function
Mehmet Zeki Sarikaya
sarikayamz@gmail.com
1
Huseyin Budak
hsyn.budak@gmail.com
2
Department of Mathematics, Faculty of Science and Arts, D\"{u}zce University, D\"{u}zce-Turkey
Department of Mathematics, Faculty of Science and Arts, D\"{u}zce University, D\"{u}zce-Turkey
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.
https://ijnaa.semnan.ac.ir/article_2797_fe30c34bcf477187700e2c4e5c003604.pdf
Generalized Hermite-Hadamard inequality
Generalized H"{o}lder inequality
Generalized convex functions
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2017-12-20
8
2
223
241
10.22075/ijnaa.2017.10778.1523
2796
Analytical aspects of the interval unilateral quadratic matrix equations and their united solution sets
Tayyebe Haqiri
thaqiri@gmail.com
1
Azim Rivaz
arivaz@uk.ac.ir
2
Mahmoud Mohseni Moghadam
mohseni@uk.ac.ir
3
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
Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
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.
https://ijnaa.semnan.ac.ir/article_2796_50bf006dbe46ff6c42b14348865a347c.pdf
AE-solution sets
interval unilateral quadratic matrix equation
united solution set
nonlinear programming
Sensitivity analysis
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2017-12-01
8
2
243
250
10.22075/ijnaa.2017.3056.1494
2767
On exponential domination and graph operations
Betul Atay
btlatay87@gmail.com
1
Aysun Aytac
aysun.aytac@ege.edu.tr
2
Department of Computer and Inst. Tech. Edu., Faculty of Education, Agri Ibrahim Cecen University, Agri, Turkey
Department of Mathematics, Faculty of Science, Ege University, 35100 Bornova-Izmir, Turkey
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.
https://ijnaa.semnan.ac.ir/article_2767_30d3be476f5e7e4708605bbc92f6406d.pdf
Graph vulnerability
network design and communication
exponential domination number
edge corona
neighbourhood corona
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2017-12-22
8
2
251
261
10.22075/ijnaa.2017.1664.1439
2766
$(varphi_1, varphi_2)$-variational principle
Abdelhakim Maaden
hmaaden2002@yahoo.fr
1
Stouti Abdelkader
stouti@yahoo.com
2
Universit\'e Sultan Moulay Slimane, Facult\'e des Sciences et Techniques, Laboratoire de Math\'ematiques et Applications, B.P. 523, Beni-Mellal 23000, Maroc
Universit\'e Sultan Moulay Slimane, Facult\'e des Sciences et Techniques, Laboratoire de Math\'ematiques et Applications, B.P. 523, Beni-Mellal 23000, Maroc
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].
https://ijnaa.semnan.ac.ir/article_2766_da52f80c47f3aee56ce7052c87770f23.pdf
$left(varphi_1, varphi_2right)$-convex function
$left(varphi_1, varphi_2right)$-variational principle
Ekeland's variational principle
smooth variational principle
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2017-12-23
8
2
263
276
10.22075/ijnaa.2017.11562.1570
2800
Existence and uniqueness of the solution for a general system of operator equations in $b-$metric spaces endowed with a graph
Cristian Chifu
cristian.chifu@tbs.ubbcluj.ro
1
Gabriela Petrusel
gabi.petrusel@tbs.ubbcluj.ro
2
Department of Business, Faculty of Business, Babes-Bolyai University, Cluj-Napoca, Romania
Department of Business, Faculty of Business, Babes-Bolyai University, Cluj-Napoca, Romania
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.
https://ijnaa.semnan.ac.ir/article_2800_62e25ec2b3418aa3f744b6478d9fbcde.pdf
Fixed point
Coupled fixed point
$b$-metric space
connected graph
integral equations
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2017-12-01
8
2
277
292
10.22075/ijnaa.2017.1476.1379
2795
Application of fractional-order Bernoulli functions for solving fractional Riccati differential equation
Yadollah Ordokhani
ordokhani@alzahra.ac.ir
1
Parisa Rahimkhani
p.rahimkhani@alzahra.ac.ir
2
Esmail Babolian
babolian@khu.ac.ir
3
Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran
Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran National Elites Foundation, Tehran, Iran
Department of Computer Science, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran
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.
https://ijnaa.semnan.ac.ir/article_2795_3990006fa9915eb0af3345e8046f7bc8.pdf
Fractional Riccati differential equation
Fractional-order Bernoulli functions
Caputo derivative
Operational matrix
Collocation method
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2017-12-01
8
2
293
306
10.22075/ijnaa.2017.11887.1594
2799
On some fixed points properties and convergence theorems for a Banach operator in hyperbolic spaces
Akindele Adebayo Mebawondu
dele@aims.ac.za
1
Lateef Jolaoso
216074984@stu.ukzn.ac.za
2
Hammed Abass
216075727@stu.ukzn.ac.za
3
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa
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.
https://ijnaa.semnan.ac.ir/article_2799_2ea33223c55fba3700f88bd7aefc3695.pdf
Banach operator
uniformly convex hyperbolic spaces
strong and $Delta$-convergence theorem
Modified Picard Normal S-iteration
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2017-12-26
8
2
307
326
10.22075/ijnaa.2016.468
468
Some common fixed point theorems for four $(psi,varphi)$-weakly contractive mappings satisfying rational expressions in ordered partial metric spaces
Rashwan Rashwan
rr_rashwan54@yahoo.com
1
S.M. Saleh
samirasaleh2007@yahoo.com
2
Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
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.
https://ijnaa.semnan.ac.ir/article_468_a5b9c5cc09ff9b3a978f98266a1b155a.pdf
Common fixed point
rational contractions
ordered partial metric spaces
dominating and dominated mappings
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2017-12-01
8
2
327
333
10.22075/ijnaa.2017.1281.1318
2786
Mazur-Ulam theorem in probabilistic normed groups
Alireza Pourmoslemi
a_pourmoslemy@pnu.ac.ir
1
Kourosh Nourouzi
nourouzi@kntu.ac.ir
2
Department of Mathematics, Payame Noor University, Tehran, Iran
Faculty of Mathematics, K.N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran
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.
https://ijnaa.semnan.ac.ir/article_2786_313d118769848a5d41636e321e9950d6.pdf
Probabilistic normed groups
Invariant probabilistic metrics
Mazur-Ulam Theorem
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2017-12-01
8
2
335
353
10.22075/ijnaa.2017.1857.1483
2787
Fixed point theorems for generalized quasi-contractions in cone $b$-metric spaces over Banach algebras without the assumption of normality with applications
Shaoyuan Xu
xushaoyuan@126.com
1
Suyu Cheng
chengsuyu1992@126.com
2
Suzana Aleksic
suzanasimic@kg.ac.rs
3
School of Mathematics and Statistics, Hanshan Normal University, Chaozhou, 521041, China
Library, Hanshan Normal University, Chaozhou, 521041, China
Department of Mathematics and Informatics, Faculty of Science, University of Kragujevac, Radoja Domanovi\'ca 12, 34000 Kragujevac, Serbia
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.
https://ijnaa.semnan.ac.ir/article_2787_c82fdf395409faa23840674b2855da21.pdf
cone $b$-metric spaces over Banach algebras
non-normal cones
$c$-sequences
generalized quasi-contractions
Fixed point theorem
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2017-12-01
8
2
355
362
10.22075/ijnaa.2017.1286.1321
2801
L$^q$ inequalities for the ${s^{th}}$ derivative of a polynomial
Ahmad Zireh
azireh@gmail.com
1
Department of Mathematics, Shahrood University of Technology, Shahrood, Iran
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.
https://ijnaa.semnan.ac.ir/article_2801_1533fb6d1e1801bc30789ab8dc04255b.pdf
Derivative
Polynomial
$L^q$ Inequality
Maximum modulus
Restricted Zeros
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2017-12-01
8
2
363
379
10.22075/ijnaa.2017.10822.1526
2794
Dynamics of higher order rational difference equation $x_{n+1}=(alpha+beta x_{n})/(A + Bx_{n}+ Cx_{n-k})$
Abu Alhalawa Muna
mabualhalawa@birzeit.edu
1
Mohammad Saleh
msaleh@birzeit.edu
2
Department of Mathematics, Faculty of Science, Birzeit University, Palestine
Department of Mathematics, Faculty of Science, Birzeit University, Palestine
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].
https://ijnaa.semnan.ac.ir/article_2794_5faa22d45bfb19c931f7a566b1d51774.pdf
stability theory
semi-cycle analysis
invariant intervals
nonlinear difference equations
discrete dynamical systems