Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171201Existence of common best proximity points of generalized $S$-proximal contractions18276410.22075/ijnaa.2017.859.1153ENHemantNashineDepartment of Mathematics, Texas A & M University-Kingsville-78363-8202, Texas, USA0000-0002-0250-9172ZoranKadelburgUniversity of Belgrade, Faculty of Mathematics, Studentski trg 16, 11000 Beograd, SerbiaJournal Article20150725In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171207On the natural stabilization of convection diffusion problems using LPIM meshless method92246610.22075/ijnaa.2016.466ENAliArefmaneshDepartment of Mechanical Engineering, University of Kashan, Kashan, IranMahmoudAbbaszadehSchool of Engineering, University of Warwick, Coventry, United KingdomJournal Article20151203By 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171203Contractive gauge functions in strongly orthogonal metric spaces232845210.22075/ijnaa.2016.452ENMaryamRamezaniDepartment of Mathematics, Faculty of Mathematics, University of Bojnord, Bojnord, IranHamidBaghaniDepartment of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, P.O. Box 98135-674, Zahedan, IranJournal Article20151107Existence 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171204Perfect $2$-colorings of the Platonic graphs293545510.22075/ijnaa.2016.455ENMohammad HadiAlaeiyanSchool of Computer Engineering, Iran University of Science and Technology, Narmak, Tehran 16846, IranHamedKaramiSchool of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846, IranJournal Article20151023In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171201Nonstandard explicit third-order Runge-Kutta method with positivity property374648010.22075/ijnaa.2016.480ENMohammadMehdizadeh KhalsaraeiDepartment of Mathematics, Faculty of Science, University of Maragheh, 55181-83111 Maragheh, IranJournal Article20141209When 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171201Curvature collineations on Lie algebroid structure476351610.22075/ijnaa.2016.516ENEsaSharahiDepartment of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, IranEsmaeilPeyghanDepartment of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, IranConstantinArcusSecondary School "Cornelius Radu", Radinesti Village, 217196 Gorj County, RomaniaJournal Article20151216Considering 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171206On the stability of linear differential equations of second order6570276810.22075/ijnaa.2017.1078.1226ENAbbasNajatiDepartment of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, IranMohammadAbdollahpourDepartment of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, IranChoonkilParkDepartment of Mathematics, Hanyang University, Seoul, 133--791, South Korea0000-0001-6329-8228Journal Article20151221The 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].Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171201Soft double fuzzy semi-topogenous structures7188278810.22075/ijnaa.2017.1787.1469ENA.GhareebDepartment of Mathematics, Colleges of Science, Al-Baha University, Al-Baha, Saudi ArabiaDepartment of Mathematics, Faculty of Science, South Valley University, Qena, EgyptO.H.KhalilDepartment of Mathematics, College of Science in Al-Zulfi, Majmaah University, Al-Zulfi, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, EgyptJournal Article20161208The 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171201Interpolation of fuzzy data by using flat end fuzzy splines8997276510.22075/ijnaa.2017.1419.1363ENRezaEzzatiDepartment of Mathematics, Karaj Branch, Islamic Azad University, Karaj, IranSaeidAbbasbandyDepartment of Applied Mathematics, Imam Khomeini International University, Qazvin, IranHosseinBehforoozDepartment of Mathematics, Utica College, Utica, New York, 13502, USAJournal Article20160603In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171201Translation invariant mappings on KPC-hypergroups99107278510.22075/ijnaa.2017.1365.1340ENSeyyed MohammadTabatabaieDepartment of Mathematics, University of Qom, Qom, IrannullFaranakHaghighifarDepartment of Mathematics, University of Qom, Qom, IranJournal Article20160430In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171201Some new Ostrowski type fractional integral inequalities for generalized $(r;g,s,m,varphi)$-preinvex functions via Caputo $k$-fractional derivatives109124279010.22075/ijnaa.2017.11722.1585ENArtionKashuriDepartment of Mathematics, Faculty of Technical Science, University "Ismail Qemali", 9400, Vlora, Albania0000-0003-0115-3079RozanaLikoDepartment of Mathematics, Faculty of Technical Science, University "Ismail Qemali", 9400, Vlora, Albania0000-0003-2439-8538Journal Article20170621In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171201Mathematical modeling of optimized SIRS epidemic model and some dynamical behavior of the solution125134279210.22075/ijnaa.2017.11821.1592ENMehdiNadjafikhahDepartment of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, IranSaeidShagholiDepartment of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, IranJournal Article20170304In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171201Modified degenerate Carlitz's $q$-bernoulli polynomials and numbers with weight ($alpha ,beta $)135144279110.22075/ijnaa.2017.11767.1588ENUgurDuranDepartment of Mathematics, Faculty of Science and Arts, University of Gaziantep, Gaziantep, 27310, Turkey0000-0002-5717-1199MehmetAcikgozDepartment of Mathematics, Faculty of Science and Arts, University of Gaziantep, Gaziantep, 27310, TurkeyJournal Article20170627The 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171201Coupled coincidence point and common coupled fixed point theorems in complex valued metric spaces14515852110.22075/ijnaa.2017.521ENFayyazRouzkardFarhangian University, Shariati Pardis, Sari, Mazandaran IranMohammadImdadDepartment of Mathematics, Aligarh Muslim University, Aligarh, 202002, IndiaJournal Article20151124In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171201Global attractor for a nonlocal hyperbolic problem on ${mathcal{R}}^{N}$159168279310.22075/ijnaa.2017.11600.1575ENPeriklesPapadopoulosDepartment of Electronics Engineering, School of Technological Applications, Piraeus University of Applied Sciences (Technological Education Institute of Piraeus), GR 11244, Egaleo, Athens, GreeceN.L.MatiadouDepartment of Electronics Engineering, School of Technological Applications, Piraeus University of Applied Sciences (Technological Education Institute of Piraeus), GR 11244, Egaleo, Athens, GreeceJournal Article20170609We 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171201Computational method based on triangular operational matrices for solving nonlinear stochastic differential equations169179278310.22075/ijnaa.2017.1023.1198ENMahnazAsgariDepartment of Engineering,~Abhar Branch,~Islamic Azad University, Abhar, IranMortezaKhodabinDepartment of Mathematics, Karaj Branch, Islamic Azad University, Karaj, IranJournal Article20151122In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171201On the approximation by Chlodowsky type generalization of (p,q)-Bernstein operators181200278910.22075/ijnaa.2017.1827.1479ENKhursheed J.AnsariDepartment of Mathematics, College of Science, King Khalid University, 61413,
Abha, Saudi ArabiaAliKaraisaDepartment of Mathematics-Computer Sciences, Faculty of Sciences, Necmettin
Erbakan University Meram Campus, 42090 Meran, Konya, TurkeyJournal Article20161227In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171201A necessary condition for multiple objective fractional programming20120748210.22075/ijnaa.2016.482ENRezvanKamaliDepartment of Mathematics, Faculty of Science, University of Isfahan, Isfahan, IranAliDavariDepartment of Mathematics, Khansar Faculty of Mathematics and Computer Science, Khansar, IranJournal Article20150119In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171201On generalized Hermite-Hadamard inequality for generalized convex function209222279710.22075/ijnaa.2017.11313.1552ENMehmet ZekiSarikayaDepartment of Mathematics, Faculty of Science and Arts, D\"{u}zce University, D\"{u}zce-TurkeyHuseyinBudakDepartment of Mathematics, Faculty of Science and Arts, D\"{u}zce University, D\"{u}zce-Turkey0000-0001-8843-955XJournal Article20170511In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171220Analytical aspects of the interval unilateral quadratic matrix equations and their united solution sets223241279610.22075/ijnaa.2017.10778.1523ENTayyebeHaqiriSchool 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, IranAzimRivazDepartment of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, IranMahmoudMohseni MoghadamDepartment of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, IranJournal Article20170307This paper introduces the<em> interval unilateral quadratic matrix equation</em>, $AX^2+BX+C=0$ and attempts to find various analytical results on its $AE$-solution sets in which $A, B$ and $C$ 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171201On exponential domination and graph operations243250276710.22075/ijnaa.2017.3056.1494ENBetulAtayDepartment of Computer and Inst. Tech. Edu., Faculty of Education, Agri Ibrahim Cecen University, Agri, TurkeyAysunAytacDepartment of Mathematics, Faculty of Science, Ege University, 35100 Bornova-Izmir, TurkeyJournal Article20170119An 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171222$(varphi_1, varphi_2)$-variational principle251261276610.22075/ijnaa.2017.1664.1439ENAbdelhakimMaadenUniversit'e Sultan Moulay Slimane, Facult'e des Sciences et Techniques, Laboratoire de Math'ematiques et Applications, B.P. 523, Beni-Mellal 23000, MaroccoStoutiAbdelkaderUniversit'e Sultan Moulay Slimane, Facult'e des Sciences et Techniques, Laboratoire de Math'ematiques et Applications, B.P. 523, Beni-Mellal 23000, MaroccoJournal Article20161013In 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].Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171223Existence and uniqueness of the solution for a general system of operator equations in $b-$metric spaces endowed with a graph263276280010.22075/ijnaa.2017.11562.1570ENCristianChifuDepartment of Business, Faculty of Business, Babes-Bolyai University, Cluj-Napoca, RomaniaGabrielaPetruselDepartment of Business, Faculty of Business, Babes-Bolyai University, Cluj-Napoca, RomaniaJournal Article20170606The 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171201Application of fractional-order Bernoulli functions for solving fractional Riccati differential equation277292279510.22075/ijnaa.2017.1476.1379ENYadollahOrdokhaniDepartment of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran0000-0002-5167-6874ParisaRahimkhaniDepartment of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran
National Elites Foundation, Tehran, IranEsmailBabolianDepartment of Computer Science, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran0000-0003-4033-3128Journal Article20160629In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171201On some fixed points properties and convergence theorems for a Banach operator in hyperbolic spaces293306279910.22075/ijnaa.2017.11887.1594ENAkindele AdebayoMebawonduSchool of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South AfricaLateefJolaosoSchool of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South AfricaHammedAbassSchool of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South AfricaJournal Article20170709In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171226Some common fixed point theorems for four $(psi,varphi)$-weakly contractive mappings satisfying rational expressions in ordered partial metric spaces30732646810.22075/ijnaa.2016.468ENRashwanRashwanDepartment of Mathematics, Faculty of Science, Assiut University, Assiut, EgyptS.M.SalehDepartment of Mathematics, Faculty of Science, Assiut University, Assiut, EgyptJournal Article20130730The 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171201Mazur-Ulam theorem in probabilistic normed groups327333278610.22075/ijnaa.2017.1281.1318ENAlirezaPourmoslemiDepartment of Mathematics, Payame Noor University, Tehran, Iran0000-0002-4008-0186KouroshNourouziFaculty of Mathematics, K.N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, IranJournal Article20160323In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171201Fixed point theorems for generalized quasi-contractions in cone $b$-metric spaces over Banach algebras without the assumption of normality with applications335353278710.22075/ijnaa.2017.1857.1483ENShaoyuanXuSchool of Mathematics and Statistics, Hanshan Normal University, Chaozhou, 521041, ChinaSuyuChengLibrary, Hanshan Normal University, Chaozhou, 521041, ChinaSuzanaAleksicDepartment of Mathematics and Informatics, Faculty of Science, University of Kragujevac, Radoja Domanovi'ca 12, 34000 Kragujevac, SerbiaJournal Article20170108In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171201L$^q$ inequalities for the ${s^{th}}$ derivative of a polynomial355362280110.22075/ijnaa.2017.1286.1321ENAhmadZirehDepartment of Mathematics, Shahrood University of Technology, Shahrood, IranJournal Article20160402Let $f(z)$ 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171201Dynamics of higher order rational difference equation $x_{n+1}=(alpha+beta x_{n})/(A + Bx_{n}+ Cx_{n-k})$363379279410.22075/ijnaa.2017.10822.1526ENAbu AlhalawaMunaDepartment of Mathematics, Faculty of Science, Birzeit University, PalestineMohammadSalehDepartment of Mathematics, Faculty of Science, Birzeit University, PalestineJournal Article20170311The 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].