Existence of common best proximity points of generalized $S$-proximal contractions
Hemant
Nashine
Department of Mathematics, Texas A \& M University-Kingsville-78363-8202, Texas, USA
author
Zoran
Kadelburg
University of Belgrade, Faculty of Mathematics, Studentski trg 16, 11000 Beograd, Serbia
author
text
article
2017
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
8
v.
2
no.
2017
1
8
https://ijnaa.semnan.ac.ir/article_2764_4a0f5785686f6c06e1cccf3bf040f1c4.pdf
dx.doi.org/10.22075/ijnaa.2017.859.1153
On the natural stabilization of convection diffusion problems using LPIM meshless method
Ali
Arefmanesh
Department of Mechanical Engineering, University of Kashan, Kashan, Iran
author
Mahmoud
Abbaszadeh
School of Engineering, University of Warwick, Coventry, United Kingdom
author
text
article
2017
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
8
v.
2
no.
2017
9
22
https://ijnaa.semnan.ac.ir/article_466_bbb3a1fc16ee7db611610410e3835c9f.pdf
dx.doi.org/10.22075/ijnaa.2016.466
Contractive gauge functions in strongly orthogonal metric spaces
Maryam
Ramezani
Department of Mathematics, Faculty of Mathematics, University of Bojnord, Bojnord, Iran
author
Hamid
Baghani
Department of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, P.O. Box 98135-674, Zahedan, Iran
author
text
article
2017
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
8
v.
2
no.
2017
23
28
https://ijnaa.semnan.ac.ir/article_452_2a1a25491ed3b19576dc43dcff80d39b.pdf
dx.doi.org/10.22075/ijnaa.2016.452
Perfect $2$-colorings of the Platonic graphs
Mohammad Hadi
Alaeiyan
School of Computer Engineering, Iran University of Science and Technology, Narmak, Tehran 16846, Iran
author
Hamed
Karami
School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846, Iran
author
text
article
2017
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
8
v.
2
no.
2017
29
35
https://ijnaa.semnan.ac.ir/article_455_b232654319dc2a0cb031bc04091ece3d.pdf
dx.doi.org/10.22075/ijnaa.2016.455
Nonstandard explicit third-order Runge-Kutta method with positivity property
Mohammad
Mehdizadeh Khalsaraei
Department of Mathematics, Faculty of Science, University of Maragheh, 55181-83111 Maragheh, Iran
author
text
article
2017
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
8
v.
2
no.
2017
37
46
https://ijnaa.semnan.ac.ir/article_480_bfe54710147d214731391df012a6a25a.pdf
dx.doi.org/10.22075/ijnaa.2016.480
Curvature collineations on Lie algebroid structure
Esa
Sharahi
Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran
author
Esmaeil
Peyghan
Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran
author
Constantin
Arcus
Secondary School "Cornelius Radu", Radinesti Village, 217196 Gorj County, Romania
author
text
article
2017
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
8
v.
2
no.
2017
47
63
https://ijnaa.semnan.ac.ir/article_516_59906f46ca9f8631db7aac16657b95ac.pdf
dx.doi.org/10.22075/ijnaa.2016.516
On the stability of linear differential equations of second order
Abbas
Najati
Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran
author
Mohammad
Abdollahpour
Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran
author
Choonkil
Park
Department of Mathematics, Hanyang University, Seoul, 133--791, South Korea
author
text
article
2017
eng
The aim of this paper is to investigate the Hyers-Ulam stability of the linear differential equation$$y''(x)+\alpha y'(x)+\beta y(x)=f(x)$$in general case, where $y\in C^2[a,b],$ $f\in C[a,b]$ 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].
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
8
v.
2
no.
2017
65
70
https://ijnaa.semnan.ac.ir/article_2768_c56749cc1ab49441e4b381aa39b132e9.pdf
dx.doi.org/10.22075/ijnaa.2017.1078.1226
Soft double fuzzy semi-topogenous structures
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
author
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
author
text
article
2017
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
8
v.
2
no.
2017
71
88
https://ijnaa.semnan.ac.ir/article_2788_42478fba2bdf9494bd980f7308e1f221.pdf
dx.doi.org/10.22075/ijnaa.2017.1787.1469
Interpolation of fuzzy data by using flat end fuzzy splines
Reza
Ezzati
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
author
Saeid
Abbasbandy
Department of Applied Mathematics, Imam Khomeini International University, Qazvin, Iran
author
Hossein
Behforooz
Department of Mathematics, Utica College, Utica, New York, 13502, USA
author
text
article
2017
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
8
v.
2
no.
2017
89
97
https://ijnaa.semnan.ac.ir/article_2765_d76b656bd725808a80f0451c76bd26b8.pdf
dx.doi.org/10.22075/ijnaa.2017.1419.1363
Translation invariant mappings on KPC-hypergroups
Seyyed Mohammad
Tabatabaie
Department of Mathematics, University of Qom, Qom, Iran
author
Faranak
Haghighifar
Department of Mathematics, University of Qom, Qom, Iran
author
text
article
2017
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
8
v.
2
no.
2017
99
107
https://ijnaa.semnan.ac.ir/article_2785_050eaa7a4eae270a339a107852a64608.pdf
dx.doi.org/10.22075/ijnaa.2017.1365.1340
Some new Ostrowski type fractional integral inequalities for generalized $(r;g,s,m,\varphi)$-preinvex functions via Caputo $k$-fractional derivatives
Artion
Kashuri
Department of Mathematics, Faculty of Technical Science, University "Ismail Qemali", 9400, Vlora, Albania
author
Rozana
Liko
Department of Mathematics, Faculty of Technical Science, University "Ismail Qemali", 9400, Vlora, Albania
author
text
article
2017
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
8
v.
2
no.
2017
109
124
https://ijnaa.semnan.ac.ir/article_2790_0b41c4fb5b26b287e9fc35c76b4ec926.pdf
dx.doi.org/10.22075/ijnaa.2017.11722.1585
Mathematical modeling of optimized SIRS epidemic model and some dynamical behavior of the solution
Mehdi
Nadjafikhah
Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, Iran
author
Saeid
Shagholi
Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, Iran
author
text
article
2017
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
8
v.
2
no.
2017
125
134
https://ijnaa.semnan.ac.ir/article_2792_035182d58bb9842edde0597201b211da.pdf
dx.doi.org/10.22075/ijnaa.2017.11821.1592
Modified degenerate Carlitz's $q$-bernoulli polynomials and numbers with weight ($\alpha ,\beta $)
Ugur
Duran
Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, Gaziantep, 27310, Turkey
author
Mehmet
Acikgoz
Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, Gaziantep, 27310, Turkey
author
text
article
2017
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
8
v.
2
no.
2017
135
144
https://ijnaa.semnan.ac.ir/article_2791_48a0eba5d8560ea93b810f1b3562b4eb.pdf
dx.doi.org/10.22075/ijnaa.2017.11767.1588
Coupled coincidence point and common coupled fixed point theorems in complex valued metric spaces
Fayyaz
Rouzkard
Farhangian University, Shariati Pardis, Sari, Mazandaran Iran
author
Mohammad
Imdad
Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India
author
text
article
2017
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
8
v.
2
no.
2017
145
158
https://ijnaa.semnan.ac.ir/article_521_2a61f222299a2c5adf3e26b8819aaa3a.pdf
dx.doi.org/10.22075/ijnaa.2017.521
Global attractor for a nonlocal hyperbolic problem on ${\mathcal{R}}^{N}$
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
author
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
author
text
article
2017
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
8
v.
2
no.
2017
159
168
https://ijnaa.semnan.ac.ir/article_2793_ef30a57e5aaa4eb687c61b37a80ea4d1.pdf
dx.doi.org/10.22075/ijnaa.2017.11600.1575
Computational method based on triangular operational matrices for solving nonlinear stochastic differential equations
Mahnaz
Asgari
Department of Engineering,~Abhar Branch,~Islamic Azad University, Abhar, Iran
author
Morteza
khodabin
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
author
text
article
2017
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
8
v.
2
no.
2017
169
179
https://ijnaa.semnan.ac.ir/article_2783_c6fbfe31fd6236b020f1a1ec4c88ae52.pdf
dx.doi.org/10.22075/ijnaa.2017.1023.1198
On the approximation by Chlodowsky type generalization of (p,q)-Bernstein operators
Khursheed
Ansari
Department of Mathematics, College of Science, King Khalid University, 61413,
Abha, Saudi Arabia
author
Ali
Karaisa
Department of Mathematics-Computer Sciences, Faculty of Sciences, Necmettin
Erbakan University Meram Campus, 42090 Meran, Konya, Turkey
author
text
article
2017
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
8
v.
2
no.
2017
181
200
https://ijnaa.semnan.ac.ir/article_2789_8c00a08033e702b77e6d822b3272f202.pdf
dx.doi.org/10.22075/ijnaa.2017.1827.1479
A necessary condition for multiple objective fractional programming
Rezvan
Kamali
Department of Mathematics, Faculty of Science, University of Isfahan, Isfahan, Iran
author
Ali
Davari
Department of Mathematics, Khansar Faculty of Mathematics and Computer Science, Khansar, Iran
author
text
article
2017
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
8
v.
2
no.
2017
201
207
https://ijnaa.semnan.ac.ir/article_482_73a53fecfb7bfc8a6778a60cabed4272.pdf
dx.doi.org/10.22075/ijnaa.2016.482
On generalized Hermite-Hadamard inequality for generalized convex function
Mehmet Zeki
Sarikaya
Department of Mathematics, Faculty of Science and Arts, D\"{u}zce University, D\"{u}zce-Turkey
author
Huseyin
Budak
Department of Mathematics, Faculty of Science and Arts, D\"{u}zce University, D\"{u}zce-Turkey
author
text
article
2017
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
8
v.
2
no.
2017
209
222
https://ijnaa.semnan.ac.ir/article_2797_fe30c34bcf477187700e2c4e5c003604.pdf
dx.doi.org/10.22075/ijnaa.2017.11313.1552
Analytical aspects of the interval unilateral quadratic matrix equations and their united solution sets
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
author
Azim
Rivaz
Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
author
Mahmoud
Mohseni Moghadam
Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
author
text
article
2017
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
8
v.
2
no.
2017
223
241
https://ijnaa.semnan.ac.ir/article_2796_50bf006dbe46ff6c42b14348865a347c.pdf
dx.doi.org/10.22075/ijnaa.2017.10778.1523
On exponential domination and graph operations
Betul
Atay
Department of Computer and Inst. Tech. Edu., Faculty of Education, Agri Ibrahim Cecen University, Agri, Turkey
author
Aysun
Aytac
Department of Mathematics, Faculty of Science, Ege University, 35100 Bornova-Izmir, Turkey
author
text
article
2017
eng
An exponential dominating set of graph $G = (V,E )$ is a subset $S\subseteq V(G)$ such that $\sum_{u\in S}(1/2)^{\overline{d}{(u,v)-1}}\geq 1$ 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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
8
v.
2
no.
2017
243
250
https://ijnaa.semnan.ac.ir/article_2767_30d3be476f5e7e4708605bbc92f6406d.pdf
dx.doi.org/10.22075/ijnaa.2017.3056.1494
$(\varphi_1, \varphi_2)$-variational principle
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
author
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
author
text
article
2017
eng
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 $\left(\varphi_1, \varphi_2\right)$-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].
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
8
v.
2
no.
2017
251
261
https://ijnaa.semnan.ac.ir/article_2766_da52f80c47f3aee56ce7052c87770f23.pdf
dx.doi.org/10.22075/ijnaa.2017.1664.1439
Existence and uniqueness of the solution for a general system of operator equations in $b-$metric spaces endowed with a graph
Cristian
Chifu
Department of Business, Faculty of Business, Babes-Bolyai University, Cluj-Napoca, Romania
author
Gabriela
Petrusel
Department of Business, Faculty of Business, Babes-Bolyai University, Cluj-Napoca, Romania
author
text
article
2017
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
8
v.
2
no.
2017
263
276
https://ijnaa.semnan.ac.ir/article_2800_62e25ec2b3418aa3f744b6478d9fbcde.pdf
dx.doi.org/10.22075/ijnaa.2017.11562.1570
Application of fractional-order Bernoulli functions for solving fractional Riccati differential equation
Yadollah
Ordokhani
Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran
author
Parisa
Rahimkhani
Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran
National Elites Foundation, Tehran, Iran
author
Esmail
Babolian
Department of Computer Science, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran
author
text
article
2017
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
8
v.
2
no.
2017
277
292
https://ijnaa.semnan.ac.ir/article_2795_3990006fa9915eb0af3345e8046f7bc8.pdf
dx.doi.org/10.22075/ijnaa.2017.1476.1379
On some fixed points properties and convergence theorems for a Banach operator in hyperbolic spaces
Akindele Adebayo
Mebawondu
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa
author
Lateef
Jolaoso
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa
author
Hammed
Abass
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa
author
text
article
2017
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
8
v.
2
no.
2017
293
306
https://ijnaa.semnan.ac.ir/article_2799_2ea33223c55fba3700f88bd7aefc3695.pdf
dx.doi.org/10.22075/ijnaa.2017.11887.1594
Some common fixed point theorems for four $(\psi,\varphi)$-weakly contractive mappings satisfying rational expressions in ordered partial metric spaces
Rashwan
Rashwan
Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
author
S.M.
Saleh
Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
author
text
article
2017
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
8
v.
2
no.
2017
307
326
https://ijnaa.semnan.ac.ir/article_468_a5b9c5cc09ff9b3a978f98266a1b155a.pdf
dx.doi.org/10.22075/ijnaa.2016.468
Mazur-Ulam theorem in probabilistic normed groups
Alireza
Pourmoslemi
Department of Mathematics, Payame Noor University, Tehran, Iran
author
Kourosh
Nourouzi
Faculty of Mathematics, K.N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran
author
text
article
2017
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
8
v.
2
no.
2017
327
333
https://ijnaa.semnan.ac.ir/article_2786_313d118769848a5d41636e321e9950d6.pdf
dx.doi.org/10.22075/ijnaa.2017.1281.1318
Fixed point theorems for generalized quasi-contractions in cone $b$-metric spaces over Banach algebras without the assumption of normality with applications
Shaoyuan
Xu
School of Mathematics and Statistics, Hanshan Normal University, Chaozhou, 521041, China
author
Suyu
Cheng
Library, Hanshan Normal University, Chaozhou, 521041, China
author
Suzana
Aleksic
Department of Mathematics and Informatics, Faculty of Science, University of Kragujevac, Radoja Domanovi\'ca 12, 34000 Kragujevac, Serbia
author
text
article
2017
eng
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 $s\ge 1$. 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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
8
v.
2
no.
2017
335
353
https://ijnaa.semnan.ac.ir/article_2787_c82fdf395409faa23840674b2855da21.pdf
dx.doi.org/10.22075/ijnaa.2017.1857.1483
L$^q$ inequalities for the ${s^{th}}$ derivative of a polynomial
Ahmad
Zireh
Department of Mathematics, Shahrood University of Technology, Shahrood, Iran
author
text
article
2017
eng
Let $f(z)$ be an analytic function on the unit disk $\{z\in\mathbb{C},\ |z|\leq 1\}$, for each $q>0$, the $\|f\|_{q}$ is defined as follows\begin{align*}\begin{split}&\left\|f\right\|_q:=\left\{\frac{1}{2\pi}\int_0^{2\pi}\left|f(e^{i\theta})\right|^qd\theta\right\}^{1/q},\\ \ 0<q<\infty,\\&\left\|f\right\|_{\infty}:=\max_{|z|=1}\left|f(z)\right|.\end{split}\end{align*} 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 $k\geq 1$, then for each $q>0$,\begin{align*}\left\|p'\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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
8
v.
2
no.
2017
355
362
https://ijnaa.semnan.ac.ir/article_2801_1533fb6d1e1801bc30789ab8dc04255b.pdf
dx.doi.org/10.22075/ijnaa.2017.1286.1321
Dynamics of higher order rational difference equation $x_{n+1}=(\alpha+\beta x_{n})/(A + Bx_{n}+ Cx_{n-k})$
Abu Alhalawa
Muna
Department of Mathematics, Faculty of Science, Birzeit University, Palestine
author
Mohammad
Saleh
Department of Mathematics, Faculty of Science, Birzeit University, Palestine
author
text
article
2017
eng
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$$x_{n+1}=\frac{\alpha+\beta x_{n}}{A + Bx_{n}+ Cx_{n-k}},~~ n=0,1,2,\ldots,$$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 $k\in\{1,2,3,\ldots\}$. 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].
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
8
v.
2
no.
2017
363
379
https://ijnaa.semnan.ac.ir/article_2794_5faa22d45bfb19c931f7a566b1d51774.pdf
dx.doi.org/10.22075/ijnaa.2017.10822.1526