2017
8
2
0
0
Existence of common best proximity points of generalized $S$proximal contractions
2
2
In this article, we introduce a new notion of proximal contraction, named as generalized Sproximal contraction and derive a common best proximity point theorem for proximally commuting nonself 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.
1

1
8


Hemant
Nashine
Department of Mathematics, Texas A & M UniversityKingsville783638202, Texas, USA
Department of Mathematics, Texas A &
Iran
drhknashine@gmail.com


Zoran
Kadelburg
University of Belgrade, Faculty of Mathematics, Studentski trg 16, 11000 Beograd, Serbia
University of Belgrade, Faculty of Mathematics,
Iran
kadelbur@matf.bg.ac.rs
common best proximity point
optimal approximate solution
proximally commuting mappings
On the natural stabilization of convection diffusion problems using LPIM meshless method
2
2
By using the finite element $p$Version in convectiondiffusion 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.
1

9
22


Ali
Arefmanesh
Department of Mechanical Engineering, University of Kashan, Kashan, Iran
Department of Mechanical Engineering, University
Iran
arefmanesh@kashanu.ac.ir


Mahmoud
Abbaszadeh
School of Engineering, University of Warwick, Coventry, United Kingdom
School of Engineering, University of Warwick,
Iran
m.abbaszadeh@warwick.ac.uk
convectiondiffusion problems
LPIM meshless method
natural stabilization
$p$Version finite element method
Contractive gauge functions in strongly orthogonal metric spaces
2
2
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.
1

23
28


Maryam
Ramezani
Department of Mathematics, Faculty of Mathematics, University of Bojnord, Bojnord, Iran
Department of Mathematics, Faculty of Mathematics,
Iran
mar.ram.math@gmail.com


Hamid
Baghani
Department of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, P.O. Box 98135674, Zahedan, Iran
Department of Mathematics, Faculty of Mathematics,
Iran
h.baghani@gmail.com
strongly orthogonal set
fixed point
gauge function
Perfect $2$colorings of the Platonic graphs
2
2
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.
1

29
35


Mohammad Hadi
Alaeiyan
School of Computer Engineering, Iran University of Science and Technology, Narmak, Tehran 16846, Iran
School of Computer Engineering, Iran University
Iran
hadi_alaeiyan@comp.iust.ac.ir


Hamed
Karami
School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846, Iran
School of Mathematics, Iran University of
Iran
h_karami@iust.ac.ir
Perfect Coloring
Equitable Partition
Platonic Graph
Nonstandard explicit thirdorder RungeKutta method with positivity property
2
2
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 thirdorder RungeKutta 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.
1

37
46


Mohammad
Mehdizadeh Khalsaraei
Department of Mathematics, Faculty of Science, University of Maragheh, 5518183111 Maragheh, Iran
Department of Mathematics, Faculty of Science,
Iran
muhammad.mehdizadeh@gmail.com
Positivity
Initial value problems
Advection equation
Bergers' equation
RungeKutta methods
Curvature collineations on Lie algebroid structure
2
2
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.
1

47
63


Esa
Sharahi
Department of Mathematics, Faculty of Science, Arak University, Arak 3815688349, Iran
Department of Mathematics, Faculty of Science,
Iran
esasharahi@gmail.com


Esmaeil
Peyghan
Department of Mathematics, Faculty of Science, Arak University, Arak 3815688349, Iran
Department of Mathematics, Faculty of Science,
Iran
epeyghan@gmail.com


Constantin
Arcus
Secondary School "Cornelius Radu", Radinesti Village, 217196 Gorj County, Romania
Secondary School "Cornelius Radu",
Iran
c_arcus@radinesti.ro
Curvature collineation
Lie algebroid
Lie symmetry
projectable section
spray
On the stability of linear differential equations of second order
2
2
The aim of this paper is to investigate the HyersUlam stability of the linear differential equation$$y''(x)+alpha y'(x)+beta y(x)=f(x)$$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{HyersUlam stability of linear differential equations of second order,} Appl. Math. Lett. 23 (2010) 306309].
1

65
70


Abbas
Najati
Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 5619911367, Iran
Department of Mathematics, Faculty of Sciences,
Iran
a.nejati@yahoo.com


Mohammad
Abdollahpour
Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 5619911367, Iran
Department of Mathematics, Faculty of Sciences,
Iran
mrabdollahpour@yahoo.com


Choonkil
Park
Department of Mathematics, Hanyang University, Seoul, 133791, South Korea
Department of Mathematics, Hanyang University,
Iran
baak@hanyang.ac.kr
HyersUlam stability
linear differential equation of second order
Soft double fuzzy semitopogenous structures
2
2
The purpose of this paper is to introduce the concept of soft double fuzzy semitopogenous order. Firstly, we give the definition of soft double fuzzy semitopogenous order. Secondly, we induce a soft double fuzzy topology from a given soft double fuzzy semitopogenous order by using soft double fuzzy interior operator.
1

71
88


A.
Ghareeb
Department of Mathematics, Colleges of Science, AlBaha University, AlBaha, Saudi Arabia
Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt
Department of Mathematics, Colleges of Science,
Iran
a.ghareeb@sci.svu.edu.eg


O.H.
Khalil
Department of Mathematics, College of Science in AlZulfi, Majmaah University, AlZulfi, Saudi Arabia
Department of Mathematics, Faculty of Science, BeniSuef University, BeniSuef, Egypt
Department of Mathematics, College of Science
Iran
nasserfuzt@hotmail.com
soft double fuzzy topology
soft double fuzzy interior operator
soft double fuzzy semitopogenous structure
Interpolation of fuzzy data by using flat end fuzzy splines
2
2
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.
1

89
97


Reza
Ezzati
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
Department of Mathematics, Karaj Branch,
Iran
ezati@kiau.ac.ir


Saeid
Abbasbandy
Department of Applied Mathematics, Imam Khomeini International University, Qazvin, Iran
Department of Applied Mathematics, Imam Khomeini
Iran
abbasbandy@yahoo.com


Hossein
Behforooz
Department of Mathematics, Utica College, Utica, New York, 13502, USA
Department of Mathematics, Utica College,
Iran
hbehforooz@utica.edu
fuzzy interpolation
extension principle
fuzzy splines
Translation invariant mappings on KPChypergroups
2
2
In this paper, we give an extension of the Wendel's theorem on KPChypergroups. We also show that every translation invariant mapping is corresponding with a unique positive measure on the KPChypergroup.
1

99
107


Seyyed Mohammad
Tabatabaie
Department of Mathematics, University of Qom, Qom, Iran
Department of Mathematics, University of
Iran
sm.tabatabaie@qom.ac.ir


Faranak
Haghighifar
Department of Mathematics, University of Qom, Qom, Iran
Department of Mathematics, University of
Iran
f.haghighifar@yahoo.com
DJShypergroup
KPChypergroup
Translation Invariant Mapping
Wendel's Theorem
Some new Ostrowski type fractional integral inequalities for generalized $(r;g,s,m,varphi)$preinvex functions via Caputo $k$fractional derivatives
2
2
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.
1

109
124


Artion
Kashuri
Department of Mathematics, Faculty of Technical Science, University "Ismail Qemali", 9400, Vlora, Albania
Department of Mathematics, Faculty of Technical
Iran
artionkashuri@gmail.com


Rozana
Liko
Department of Mathematics, Faculty of Technical Science, University "Ismail Qemali", 9400, Vlora, Albania
Department of Mathematics, Faculty of Technical
Iran
rozanaliko86@gmail.com
Ostrowski type inequality
H"{o}lder's inequality
Minkowski's inequality
$s$convex function in the second sense
$m$invex
Mathematical modeling of optimized SIRS epidemic model and some dynamical behavior of the solution
2
2
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 RungeKutta method is applied to the nonlinear system of differential equations.
1

125
134


Mehdi
Nadjafikhah
Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 1684613114, Iran
Department of Pure Mathematics, School of
Iran
m_nadjafikhah@iust.ac.ir


Saeid
Shagholi
Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 1684613114, Iran
Department of Pure Mathematics, School of
Iran
sshagholi@mathdep.iust.ac.ir
Mathematical modeling
epidemic SIRS model
positive solution
globally asymptotically stability
Modified degenerate Carlitz's $q$bernoulli polynomials and numbers with weight ($alpha ,beta $)
2
2
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.
1

135
144


Ugur
Duran
Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, Gaziantep, 27310, Turkey
Department of Mathematics, Faculty of Science
Iran
mtdrnugur@gmail.com


Mehmet
Acikgoz
Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, Gaziantep, 27310, Turkey
Department of Mathematics, Faculty of Science
Iran
acikgoz@gantep.edu.tr
Carlitz's $q$Bernoulli polynomials
Stirling numbers of the first kind
Stirling numbers of the second kind
$p$adic $q$integral
Coupled coincidence point and common coupled fixed point theorems in complex valued metric spaces
2
2
In this paper, we introduce the concept of a wcompatible 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.
1

145
158


Fayyaz
Rouzkard
Farhangian University, Shariati Pardis, Sari, Mazandaran Iran
Farhangian University, Shariati Pardis, Sari,
Iran
fayyazrouzkard@gmail.com


Mohammad
Imdad
Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India
Department of Mathematics, Aligarh Muslim
Iran
mhimdad@yahoo.co.in
Common fixed point
Contractive type mapping
coupled coincidence point
coupled point of coincidence
Complex valued metric space
Global attractor for a nonlocal hyperbolic problem on ${mathcal{R}}^{N}$
2
2
We consider the quasilinear Kirchhoff's problem$$ u_{tt}phi (x)nabla u(t)^{2}Delta u+f(u)=0 ,;; x in {mathcal{R}}^{N}, ;; t geq 0,$$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.
1

159
168


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
Department of Electronics Engineering, School
Iran
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
Department of Electronics Engineering, School
Iran
lmatiadou@yahoo.gr
quasilinear hyperbolic equations
Kirchhoff strings
global attractor
generalised Sobolev spaces
weighted $L^p$ Spaces
Computational method based on triangular operational matrices for solving nonlinear stochastic differential equations
2
2
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.
1

169
179


Mahnaz
Asgari
Department of Engineering,~Abhar Branch,~Islamic Azad University, Abhar, Iran
Department of Engineering,~Abhar Branch,~Islamic
Iran
mah_sgr@yahoo.com


Morteza
khodabin
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
Department of Mathematics, Karaj Branch,
Iran
mkhodabin@kiau.ac.ir
Brownian motion
It^{o} integral
Nonlinear stochastic differential equation
Stochastic operational matrix
Triangular function
On the approximation by Chlodowsky type generalization of (p,q)Bernstein operators
2
2
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.
1

181
200


Khursheed
Ansari
Department of Mathematics, College of Science, King Khalid University, 61413,
Abha, Saudi Arabia
Department of Mathematics, College of Science,
Iran
ansari.jkhursheed@gmail.com


Ali
Karaisa
Department of MathematicsComputer Sciences, Faculty of Sciences, Necmettin
Erbakan University Meram Campus, 42090 Meran, Konya, Turkey
Department of MathematicsComputer Sciences,
Iran
akaraisa@konya.edu.tr
$(p,q)$integers
Bernstein operators
positive linear operators
Korovkin type approximation theorem
statistical approximation
A necessary condition for multiple objective fractional programming
2
2
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.
1

201
207


Rezvan
Kamali
Department of Mathematics, Faculty of Science, University of Isfahan, Isfahan, Iran
Department of Mathematics, Faculty of Science,
Iran
reka_math@yahoo.com


Ali
Davari
Department of Mathematics, Khansar Faculty of Mathematics and Computer Science, Khansar, Iran
Department of Mathematics, Khansar Faculty
Iran
a_davari2002@yahoo.com
Multiple objective fractional programming
Generalized nset convex function
Efficient solution
On generalized HermiteHadamard inequality for generalized convex function
2
2
In this paper, a new inequality for generalized convex functions which is related to the left side of generalized HermiteHadamard type inequality is obtained. Some applications for some generalized special means are also given.
1

209
222


Mehmet Zeki
Sarikaya
Department of Mathematics, Faculty of Science and Arts, D"{u}zce University, D"{u}zceTurkey
Department of Mathematics, Faculty of Science
Iran
sarikayamz@gmail.com


Huseyin
Budak
Department of Mathematics, Faculty of Science and Arts, D"{u}zce University, D"{u}zceTurkey
Department of Mathematics, Faculty of Science
Iran
hsyn.budak@gmail.com
Generalized HermiteHadamard inequality
Generalized H"{o}lder inequality
Generalized convex functions
Analytical aspects of the interval unilateral quadratic matrix equations and their united solution sets
2
2
This paper introduces the emph{interval unilateral quadratic matrix equation}, $IUQe$ and attempts to find various analytical results on its AEsolution 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 nonemptiness of some quasisolution 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.
1

223
241


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 7616914111, Iran
School of Mathematics and Computer Science,
Iran
thaqiri@gmail.com


Azim
Rivaz
Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
Department of Applied Mathematics, Faculty
Iran
arivaz@uk.ac.ir


Mahmoud
Mohseni Moghadam
Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
Department of Applied Mathematics, Faculty
Iran
mohseni@uk.ac.ir
AEsolution sets
interval unilateral quadratic matrix equation
united solution set
nonlinear programming
Sensitivity Analysis
On exponential domination and graph operations
2
2
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.
1

243
250


Betul
Atay
Department of Computer and Inst. Tech. Edu., Faculty of Education, Agri Ibrahim Cecen University, Agri, Turkey
Department of Computer and Inst. Tech. Edu.,
Iran
btlatay87@gmail.com


Aysun
Aytac
Department of Mathematics, Faculty of Science, Ege University, 35100 BornovaIzmir, Turkey
Department of Mathematics, Faculty of Science,
Iran
aysun.aytac@ege.edu.tr
Graph vulnerability
network design and communication
exponential domination number
edge corona
neighbourhood corona
$(varphi_1, varphi_2)$variational principle
2
2
In this paper we prove that if $X $ is a Banach space, then for every lower semicontinuous 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 wellknown varitional principles as that of Ekeland [On the variational principle, J. Math. Anal. Appl. 47 (1974) 323353], that of BorweinPreiss [A smooth variational principle with applications to subdifferentiability and to differentiability of convex functions, Trans. Amer. Math. Soc. 303 (1987) 517527] and that of DevilleGodefroyZizler [Un principe variationel utilisant des fonctions bosses, C. R. Acad. Sci. (Paris). Ser.I 312 (1991) 281286] and [A smooth variational principle with applications to HamiltonJacobi equations in infinite dimensions, J. Funct. Anal. 111 (1993) 197212].
1

251
261


Abdelhakim
Maaden
Universit'e Sultan Moulay Slimane, Facult'e des Sciences et Techniques, Laboratoire de Math'ematiques et Applications, B.P. 523, BeniMellal 23000, Maroc
Universit'e Sultan Moulay Slimane,
Iran
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, BeniMellal 23000, Maroc
Universit'e Sultan Moulay Slimane,
Iran
stouti@yahoo.com
$left(varphi_1, varphi_2right)$convex function
$left(varphi_1, varphi_2right)$variational principle
Ekeland's variational principle
smooth variational principle
Existence and uniqueness of the solution for a general system of operator equations in $b$metric spaces endowed with a graph
2
2
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, wellposedness and UlamHyers 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.
1

263
276


Cristian
Chifu
Department of Business, Faculty of Business, BabesBolyai University, ClujNapoca, Romania
Department of Business, Faculty of Business,
Iran
cristian.chifu@tbs.ubbcluj.ro


Gabriela
Petrusel
Department of Business, Faculty of Business, BabesBolyai University, ClujNapoca, Romania
Department of Business, Faculty of Business,
Iran
gabi.petrusel@tbs.ubbcluj.ro
fixed point
coupled fixed point
$b$metric space
connected graph
integral equations
Application of fractionalorder Bernoulli functions for solving fractional Riccati differential equation
2
2
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 fractionalorder Bernoulli functions approximations. First, the fractionalorder 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.
1

277
292


Yadollah
Ordokhani
Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran
Department of Mathematics, Faculty of Mathematical
Iran
ordokhani@alzahra.ac.ir


Parisa
Rahimkhani
Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran
National Elites Foundation, Tehran, Iran
Department of Mathematics, Faculty of Mathematical
Iran
p.rahimkhani@alzahra.ac.ir


Esmail
Babolian
Department of Computer Science, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran
Department of Computer Science, Faculty of
Iran
babolian@khu.ac.ir
Fractional Riccati differential equation
Fractionalorder Bernoulli functions
Caputo derivative
Operational matrix
Collocation method
On some fixed points properties and convergence theorems for a Banach operator in hyperbolic spaces
2
2
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.
1

293
306


Akindele Adebayo
Mebawondu
School of Mathematics, Statistics and Computer Science, University of KwaZuluNatal, Durban, South Africa
School of Mathematics, Statistics and Computer
Iran
dele@aims.ac.za


Lateef
Jolaoso
School of Mathematics, Statistics and Computer Science, University of KwaZuluNatal, Durban, South Africa
School of Mathematics, Statistics and Computer
Iran
216074984@stu.ukzn.ac.za


Hammed
Abass
School of Mathematics, Statistics and Computer Science, University of KwaZuluNatal, Durban, South Africa
School of Mathematics, Statistics and Computer
Iran
216075727@stu.ukzn.ac.za
Banach operator
uniformly convex hyperbolic spaces
strong and $Delta$convergence theorem
Modified Picard Normal Siteration
Some common fixed point theorems for four $(psi,varphi)$weakly contractive mappings satisfying rational expressions in ordered partial metric spaces
2
2
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 wellknown results in the literature. Also, we give two examples to illustrate our results.
1

307
326


Rashwan
Rashwan
Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
Department of Mathematics, Faculty of Science,
Iran
rr_rashwan54@yahoo.com


S.M.
Saleh
Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
Department of Mathematics, Faculty of Science,
Iran
samirasaleh2007@yahoo.com
Common fixed point
rational contractions
ordered partial metric spaces
dominating and dominated mappings
MazurUlam theorem in probabilistic normed groups
2
2
In this paper, we give a probabilistic counterpart of MazurUlam theorem in probabilistic normed groups. We show, under some conditions, that every surjective isometry between two probabilistic normed groups is a homomorphism.
1

327
333


Alireza
Pourmoslemi
Department of Mathematics, Payame Noor University, Tehran, Iran
Department of Mathematics, Payame Noor University,
Iran
a_pourmoslemy@pnu.ac.ir


Kourosh
Nourouzi
Faculty of Mathematics, K.N. Toosi University of Technology, P.O. Box 163151618, Tehran, Iran
Faculty of Mathematics, K.N. Toosi University
Iran
nourouzi@kntu.ac.ir
Probabilistic normed groups
Invariant probabilistic metrics
MazurUlam Theorem
Fixed point theorems for generalized quasicontractions in cone $b$metric spaces over Banach algebras without the assumption of normality with applications
2
2
In this paper, we introduce the concept of generalized quasicontractions 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 quasicontractions with the spectral radius $r(lambda)$ of the quasicontractive 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 $g$quasicontractions in the setting of such spaces. The main results generalize, extend and unify several wellknown 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.
1

335
353


Shaoyuan
Xu
School of Mathematics and Statistics, Hanshan Normal University, Chaozhou, 521041, China
School of Mathematics and Statistics, Hanshan
Iran
xushaoyuan@126.com


Suyu
Cheng
Library, Hanshan Normal University, Chaozhou, 521041, China
Library, Hanshan Normal University, Chaozhou,
Iran
chengsuyu1992@126.com


Suzana
Aleksic
Department of Mathematics and Informatics, Faculty of Science, University of Kragujevac, Radoja Domanovi'ca 12, 34000 Kragujevac, Serbia
Department of Mathematics and Informatics,
Iran
suzanasimic@kg.ac.rs
cone $b$metric spaces over Banach algebras
nonnormal cones
$c$sequences
generalized quasicontractions
fixed point theorem
L$^q$ inequalities for the ${s^{th}}$ derivative of a polynomial
2
2
Let $f(z)$ be an analytic function on the unit disk ${zinmathbb{C}, zleq 1}$, for each $q>0$, the $f_{q}$ is defined as followsbegin{align*}begin{split}&leftfright_q:=left{frac{1}{2pi}int_0^{2pi}leftf(e^{itheta})right^qdthetaright}^{1/q},\ 0<q<infty,\&leftfright_{infty}:=max_{z=1}leftf(z)right.end{split}end{align*} Govil and Rahman [{it Functions of exponential type not vanishing in a halfplane and related polynomials}, { Trans. Amer. Math. Soc.} {137} (1969) 501517] proved that if $p(z)$ is a polynomial of degree $n$, which does not vanish in $z<k$, where $kgeq 1$, then for each $q>0$,begin{align*}leftp'right_{q}leq frac{n}{k+z_q}p_{q}.end{align*}In this paper, we shall present an interesting generalization and refinement of this result which include some previous results.
1

355
362


Ahmad
Zireh
Department of Mathematics, Shahrood University of Technology, Shahrood, Iran
Department of Mathematics, Shahrood University
Iran
azireh@gmail.com
Derivative
Polynomial
$L^q$ Inequality
Maximum modulus
Restricted Zeros
Dynamics of higher order rational difference equation $x_{n+1}=(alpha+beta x_{n})/(A + Bx_{n}+ Cx_{nk})$
2
2
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$$x_{n+1}=frac{alpha+beta x_{n}}{A + Bx_{n}+ Cx_{nk}},~~ n=0,1,2,ldots,$$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 semicycles 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 $x_{n+1}=frac{alpha +beta x_{n}}{A+Bx_{n}+ C x_{n1}}$, Facts and Conjectures, Comput. Math. Appl. 45 (2003) 10871099].
1

363
379


Abu Alhalawa
Muna
Department of Mathematics, Faculty of Science, Birzeit University, Palestine
Department of Mathematics, Faculty of Science,
Iran
mabualhalawa@birzeit.edu


Mohammad
Saleh
Department of Mathematics, Faculty of Science, Birzeit University, Palestine
Department of Mathematics, Faculty of Science,
Iran
msaleh@birzeit.edu
stability theory
semicycle analysis
invariant intervals
nonlinear difference equations
discrete dynamical systems