Existence of Solutions for some Nonlinear Volterra Integral Equations via Petryshyn's Fixed Point Theorem Manouchehr Kazemi Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran author Reza Ezzati Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran author text article 2018 eng In this paper, we study the existence of solutions of some nonlinear Volterra integral equations by using the techniques of measures of noncompactness and the Petryshyn's fixed point theorem in Banach space. We also present some examples of the integral equation to confirm the efficiency of our results. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 9 v. 1 no. 2018 1 12 https://ijnaa.semnan.ac.ir/article_2296_80fd65a54d2078b7f30046da57777be0.pdf dx.doi.org/10.22075/ijnaa.2017.1394.1352 Decomposition of supra soft locally closed sets and supra SLC-continuity Alaa Abd El-latif Mathematics Department, Faculty of Arts and Science, Northern Border University, Rafha, Saudi Arabia author text article 2018 eng In this paper, we introduce two different notions of generalized supra soft sets namely supra A--soft sets and supra soft locally closed sets in supra soft topological spaces, which are weak forms of supra open soft sets and discuss their relationships with each other and other supra open soft sets [International Journal of Mathematical Trends and Technology, (IJMTT), (2014) Vol. 9 (1): 37-56] like supra semi open soft sets, supra pre open soft sets, supra $\alpha$-open sets and supra $\beta$--open sets. Furthermore, the soft union and intersection of two supra soft locally closed sets have been obtained. We also introduce two different notions of generalized supra soft continuity namely supra soft A-continuous functions and supra SLC-continuous functions. Finally, we obtain decompositions of supra soft continuity: $f_{pu}$ is a supra soft A-continuous if it is both supra soft semi-continuous and supra SLC-continuous, and also $f_{pu}$ is a supra soft continuous if and only if it is both supra soft pre-continuous and supra SLC-continuous. Several examples are provided to illustrate the behavior of these new classes of supra soft sets and supra soft functions. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 9 v. 1 no. 2018 13 25 https://ijnaa.semnan.ac.ir/article_3079_0ce2a60a6abf1f556e2f1984a2737b0d.pdf dx.doi.org/10.22075/ijnaa.2018.12727.1651 Strong convergence theorem for a class of multiple-sets split variational inequality problems in Hilbert spaces Chinedu Izuchukwu School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa author text article 2018 eng In this paper, we introduce a new iterative algorithm for approximating a common solution of certain class of multiple-sets split variational inequality problems. The sequence of the proposed iterative algorithm is proved to converge strongly in Hilbert spaces. As application, we obtain some strong convergence results for some classes of multiple-sets split convexminimization problems. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 9 v. 1 no. 2018 27 40 https://ijnaa.semnan.ac.ir/article_3080_cbdad3d80d8f73b4f043cf6b8daff31e.pdf dx.doi.org/10.22075/ijnaa.2018.12463.1632 Lie ternary $(\sigma,\tau,\xi)$--derivations on Banach ternary algebras Razieh Farokhzad Rostami Department of Mathematics, Faculty of Basic Sciences and Engineering, Gonbad Kavous University, Gonbad Kavous, Iran author text article 2018 eng Let $A$ be a Banach ternary algebra over a scalar field $\Bbb R$ or $\Bbb C$ and $X$ be a ternary Banach $A$--module. Let $\sigma,\tau$ and $\xi$ be linear mappings on $A$, a linear mapping $D:(A,[~]_A)\to (X,[~]_X)$ is called a Lie ternary $(\sigma,\tau,\xi)$--derivation, if $$D([a,b,c])=[[D(a)bc]_X]_{(\sigma,\tau,\xi)}-[[D(c)ba]_X]_{(\sigma,\tau,\xi)}$$ for all $a,b,c\in A$, where $[abc]_{(\sigma,\tau,\xi)}=a\tau(b)\xi(c)-\sigma(c)\tau(b)a$ and $[a,b,c]=[abc]_{A}-[cba]_{A}$. In this paper, we prove the generalized Hyers--Ulam--Rassias stability of Lie ternary $(\sigma,\tau,\xi)$--derivations on Banach ternary algebras and $C^*$--Lie ternary $(\sigma,\tau,\xi)$--derivations on $C^*$--ternary algebras for the following Euler--Lagrange type additive mapping: $$\sum_{i=1}^{n}f\textbf{(}\sum_{j=1}^{n}q(x_i-x_j)\textbf{)} +nf(\sum_{i=1}^{n}qx_i)=nq\sum_{i=1}^{n}f(x_i).$$ International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 9 v. 1 no. 2018 41 53 https://ijnaa.semnan.ac.ir/article_3081_6486c63f9dfbcbb69da5dc4438109c41.pdf dx.doi.org/10.22075/ijnaa.2018.3081 Fekete-Szeg\"o problems for analytic functions in the space of logistic sigmoid functions based on quasi-subordination Murugusundaramoorthy Gangadharan Dr. G. Murugusundaramoorthy, Ph.D. Sr.Professor of Mathematics, School of Advanced Sciences, VIT University, Vellore 632 014 India author Sunday Oluwafemi Olatunji Department of Mathematical Sciences, Federal University of Technology, Akure, Nigeria author O.A. Fadipe-Joseph Department of Mathematics, University of Ilorin, P.M.B. 1515 Ilorin, Nigeria author text article 2018 eng In this paper, we define new subclasses ${S}^{*}_{q}(\alpha,\Phi),$ ${M}_{q}(\alpha,\Phi)$ and ${L}_{q}(\alpha,\Phi)$ of analytic functions in the space of logistic sigmoid functions based on quasi--subordination and determine the initial coefficient estimates $|a_2|$ and $|a_3|$ and also determine the relevant connection to the classical Fekete-Szego inequalities. Further, we discuss the improved results for the associated classes involving subordination and majorization results briefly. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 9 v. 1 no. 2018 55 68 https://ijnaa.semnan.ac.ir/article_3082_32c7c0a2eb966732ef665b9730390061.pdf dx.doi.org/10.22075/ijnaa.2018.11778.1589 On Hadamard and Fej\'{e}r-Hadamard inequalities for Caputo $\small{k}$-fractional derivatives Ghulam Farid Mathematics Department, COMSATS Institute of Information Technology, Attock Campus, Attock, Pakistan author Anum Javed Mathematics, COMSATS Institute of Information Technology, Attock Campus, Attock, Pakistan author text article 2018 eng In this paper we will prove certain Hadamard and Fejer-Hadamard inequalities for the functions whose nth derivatives are convex by using Caputo k-fractional derivatives. These results have some relationship with inequalities for Caputo fractional derivatives. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 9 v. 1 no. 2018 69 81 https://ijnaa.semnan.ac.ir/article_3083_b8b7d30ba725674609012789386a7b89.pdf dx.doi.org/10.22075/ijnaa.2018.10724.1521 Dynamic system of strategic games Madjid Eshaghi Gordji Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan 35195-363, Iran author Gholamreza Askari Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan 35195-363, Iran author text article 2018 eng Maybe an event can't be modeled completely through one game but there is more chance with several games. With emphasis on players' rationality, we present new properties of strategic games, which result in production of other games. Here, a new attitude to modeling will be presented in game theory as dynamic system of strategic games and its some applications such as analysis of the clash between the United States and Iran in Iraq will be provided. In this system with emphasis on players’ rationality, the relationship between strategic games and explicitly the dynamics present in interactions among players will be examined. In addition, we introduce a new game called trickery game. This game shows a good reason for the cunning of some people in everyday life. Cooperation is a hallmark of human society. In many cases, our study provides a mechanism to move towards cooperation between players. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 9 v. 1 no. 2018 83 98 https://ijnaa.semnan.ac.ir/article_2706_4ba202a0aba8f61e2a61ec9d80aa3be9.pdf dx.doi.org/10.22075/ijnaa.2017.12774.1657 Influences of magnetic field in viscoelastic fluid Kashif Abro Department of Mathematics, NED University of Engineering Technology, Karachi, Pakistan author Mirza Baig Department of Mathematics, NED University of Engineering Technology, Karachi, Pakistan author Mukruram Hussain Institute of Space Technology, Karachi, Pakistan author text article 2018 eng This communication influences on magnetohydrodynamic flow of viscoelastic fluid with magnetic field induced by oscillating plate. General solutions have been found out for velocity and shear stress profiles using mathematical transformations (Integral transforms). The governing partial differential equations have been solved analytically under boundary conditions u(0,t)=A_0 H(t)sinΩt and u(0,t)=A_0 H(t)cosΩt with t≥0. For the sake of simplicity of boundary conditions are verified on the analytical general solutions and similar solutions have been particularized under three limited cases namely (i). Maxwell fluid with out magnetic field if γ≠0,M=0 (ii). Newtonian fluid with magnetic field if γ=0,M≠0 and (iii). Newtonian fluid with out magnetic field if γ=0,M=0. Finally various physical parameters with variations of fluid behaviors are analyzed and depicted graphical illustrations. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 9 v. 1 no. 2018 99 109 https://ijnaa.semnan.ac.ir/article_3085_6452f001f824094059a183987374f4a3.pdf dx.doi.org/10.22075/ijnaa.2017.1451.1367 Local higher derivations on C*-algebras are higher derivations Lila Naranjani Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran author Mahmoud Hassani Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran author Madjid Mirzavaziri Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran author text article 2018 eng Let $\mathfrak{A}$ be a Banach algebra. We say that a sequence $\{D_n\}_{n=0}^\infty$ of continuous operators form $\mathfrak{A}$ into $\mathfrak{A}$ is a \textit{local higher derivation} if to each $a\in\mathfrak{A}$ there corresponds a continuous higher derivation $\{d_{a,n}\}_{n=0}^\infty$ such that $D_n(a)=d_{a,n}(a)$ for each non-negative integer $n$. We show that if $\mathfrak{A}$ is a $C^*$-algebra then each local higher derivation on $\mathfrak{A}$ is a higher derivation. We also prove that each local higher derivation on a $C^*$-algebra is automatically continuous. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 9 v. 1 no. 2018 111 115 https://ijnaa.semnan.ac.ir/article_3098_2dd5a1ec2b9eb291b3144ecc1e96595e.pdf dx.doi.org/10.22075/ijnaa.2018.3098 Numerical resolution of large deflections in cantilever beams by Bernstein spectral method and a convolution quadrature. Mohammadkeya khosravi Institute of Applied Mechanics, Graz University of Technology, Technikerstrasse 4, 8010 Graz, Austria author Mostafa Jani Department of Mathematics, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran author text article 2018 eng The mathematical modeling of the large deflections for the cantilever beams leads to a nonlinear differential equation with the mixed boundary conditions. Different numerical methods have been implemented by various authors for such problems. In this paper, two novel numerical techniques are investigated for the numerical simulation of the problem. The first is based on a spectral method utilizing modal Bernstein polynomial basis. This gives a polynomial expression for the beam configuration. To do so, a polynomial basis satisfying the boundary conditions is presented by using the properties of the Bernstein polynomials. In the second approach, we first transform the problem into an equivalent Volterra integral equation with a convolution kernel. Then, the second order convolution quadrature method is implemented to discretize the problem along with a finite difference approximation for the Neumann boundary condition on the free end of the beam. Comparison with the experimental data and the existing numerical and semi-analytical methods demonstrate the accuracy and efficiency of the proposed methods. Also, the numerical experiments show the Bernstein-spectral method has a spectral order of accuracy and the convolution quadrature methods equipped with a finite difference discretization gives a second order of accuracy. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 9 v. 1 no. 2018 117 127 https://ijnaa.semnan.ac.ir/article_3086_2fa91707207706c3ca97107695829a94.pdf dx.doi.org/10.22075/ijnaa.2017.11240.1549 Solutions of initial and boundary value problems via F-contraction mappings in metric-like space Hemant Kumar Nashine Department of Mathematics, Texas A & M University - Kingsville - 78363-8202, Texas, USA author Dhananjay Gopal Department of Applied Mathematics & Humanities, S.V. National Institute of Technology, Surat-395007, Gujarat, India author Dilip Jain Department of Applied Mathematics & Humanities, S.V. National Institute of Technology, Surat-395007, Gujarat, India author Ahmed Al-Rawashdeh Department of Mathematics, United Arab Emirates University, UAE author text article 2018 eng We present sufficient conditions for the existence of solutions of second-order two-point boundary value and fractional order functional differential equation problems in a space where self distance is not necessarily zero. For this, first we introduce a Ciric type generalized F-contraction and F-Suzuki contraction in a metric-like space and give relevance to fixed point results. To illustrate our results, we give throughout the paper some examples. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 9 v. 1 no. 2018 129 145 https://ijnaa.semnan.ac.ir/article_3089_b5af7b8a4b803b959039333d370da074.pdf dx.doi.org/10.22075/ijnaa.2017.1725.1452 New hybrid method for equilibrium problems and relatively nonexpansive mappings in Banach spaces Sattar Alizadeh Department of Mathematics, Marand Branch, Islamic Azad University, Marand, Iran author Fridoun Moradlou Department of Mathematics, Sahand University of Technology, Tabriz, Iran author text article 2018 eng In this paper, applying hybrid projection method, a new modified Ishikawa iteration scheme is presented for finding a common element of the solution set of an equilibrium problem and the set of fixed points of relatively nonexpansive mappings in Banach spaces. A numerical example is given and the numerical behaviour of the sequences generated by this algorithm is compared with several existence results in literature to illustrate the usability of obtained results. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 9 v. 1 no. 2018 147 159 https://ijnaa.semnan.ac.ir/article_3087_f22c8d3c0741a826a1347239994559cd.pdf dx.doi.org/10.22075/ijnaa.2018.12168.1614 Efficient elliptic curve cryptosystems Mohammad Saleh Mathematics Department, Birzeit University, P.O. Box 14, Palestine author Kamal Darweesh Applied Mathematics Department, Palestine Technical University--Kadoorie, Tulkarm, Palestine author text article 2018 eng Elliptic curve cryptosystems (ECC) are new generations of public key cryptosystems that have a smaller key size for the same level of security. The exponentiation on elliptic curve is the most important operation in ECC, so when the ECC is put into practice, the major problem is how to enhance the speed of the exponentiation. It is thus of great interest to develop algorithms for exponentiation, which allow efficient implementations of ECC. In this paper, we improve efficient algorithm for exponentiation on elliptic curves defined over Fp in terms of affine coordinates. The algorithm computes directly from random points P and Q on an elliptic curve, without computing the intermediate points. Moreover, we apply the algorithm to exponentiation on elliptic curves with width-w Mutual Opposite Form (wMOF) and analyze their computational complexity. This algorithm can speed up the wMOF exponentiation of elliptic curves of size 160-bit about (21.7 %) as a result of its implementation with respect to affine coordinates. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 9 v. 1 no. 2018 161 174 https://ijnaa.semnan.ac.ir/article_3090_0f826058d0ae814be01864ee304396ac.pdf dx.doi.org/10.22075/ijnaa.2018.11642.1581 Analysis of fully developed flow and heat transfer through n-sided polygonal ducts with round corners using the Galerkin weighted residual method Ali Akbar Abbasian Arani Department of Mechanical Engineering, Faculty of Mechanical Engineering, University of Kashan, Kashan 87317-51167, Iran author Ali Arefmanesh Department of Mechanical Engineering, Faculty of Mechanical Engineering, University of Kashan, Kashan 87317-51167, Iran author Amirhossein Niroumand Department of Mechanical Engineering, Faculty of Mechanical Engineering, University of Kashan, Kashan 87317-51167, Iran author text article 2018 eng The Galerkin weighted residuals method is extended solve the laminar, fully developed flow and heat transfer of Al2O3-water nanofluid inside polygonal ducts with round corners for the constant heat flux and uniform wall temperature boundary conditions. Using the method, semi-analytical, closed-form solutions are obtained for the friction coefficient and the Nusselt number in terms of the radius of the round corners for the triangular, rectangular, hexagonal, and octagonal ducts. The effects of varying the radius of the round corners and the volume fraction of the nanoparticles on the friction coefficient and the Nusselt number are analyzed. The results show that the friction factor and the average Nusselt number increase with increasing the radius of the round corners. The study indicates that the Galerkin weighted residuals method is an accurate and efficient technique to obtain closed-form solutions for the flow and temperature fields in ducts with complex cross sectional shapes. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 9 v. 1 no. 2018 175 193 https://ijnaa.semnan.ac.ir/article_3088_401f00e4daaf23f9740067ab22865a13.pdf dx.doi.org/10.22075/ijnaa.2017.10429.1502 (JCLR) property and fixed point in non-Archimedean fuzzy metric spaces Ismat Beg Lahore School of Economics, Lahore, Pakistan author M. Ahmed Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt author N. Nafadi Department of Mathematics, Faculty of Science, Port Said University, Port Said, Egypt author text article 2018 eng The aim of the present paper is to introduce the concept of joint common limit range property ((JCLR) property) for single-valued and set-valued maps in non-Archimedean fuzzy metric spaces. We also list some examples to show the difference between (CLR) property and (JCLR) property. Further, we establish common fixed point theorems using implicit relation with integral contractive condition. Several examples to illustrate the significance of our results are given. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 9 v. 1 no. 2018 195 201 https://ijnaa.semnan.ac.ir/article_3092_2f1f766d89f68e23e74e6d57c2a062e0.pdf dx.doi.org/10.22075/ijnaa.2018.10861.1529 Endpoints of multi-valued cyclic contraction mappings Sirous Moradi Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran author text article 2018 eng Endpoint results are presented for multi-valued cyclic contraction mappings on complete metric spaces (X, d). Our results extend previous results given by Nadler (1969), Daffer-Kaneko (1995), Harandi (2010), Moradi and Kojasteh (2012) and Karapinar (2011). International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 9 v. 1 no. 2018 203 210 https://ijnaa.semnan.ac.ir/article_3093_e6242ec1c326609daf7f125e152ae988.pdf dx.doi.org/10.22075/ijnaa.2018.3093 Fractional Hermite-Hadamard type inequalities for n-times log-convex functions Nawel Ouanas Departement des Mathematiques, Faculte des Mathematiques, de l&#039;informatique et des sciences de la matiere, Universite 8 May 1945 Guelma, Algeria author Badreddine Meftah Laboratoire des tecommunications, Faculte des Sciences et de la Technologie, University of 8 May 1945 Guelma, P.O. Box 401, 24000 Guelma, Algeria. author Meriem Merad Departement des Mathematiques, Faculte des Mathematiques, de l&#039;informatique et des sciences de la matiere, Universite 8 May 1945 Guelma, Algeria author text article 2018 eng In this paper, we establish some Hermite-Hadamard type inequalities for function whose n-th derivatives are logarithmically convex by using Riemann-Liouville integral operator. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 9 v. 1 no. 2018 211 221 https://ijnaa.semnan.ac.ir/article_3094_ca41a655282c9d139a02d65706aa0d5c.pdf dx.doi.org/10.22075/ijnaa.2018.12016.1601 A new approximation method for common fixed points of a finite family of nonexpansive non-self mappings in Banach spaces Pornsak Yatakoat Division of Mathematics, Faculty of Sciences, Nakhon Phanom University, Nakhon Phanom 48000, Thailand author text article 2018 eng In this paper, we introduce a new iterative scheme to approximate a common fixed point for a finite family of nonexpansive non-self mappings. Strong convergence theorems of the proposed iteration in Banach spaces. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 9 v. 1 no. 2018 223 234 https://ijnaa.semnan.ac.ir/article_3095_d8a45ff392ad80350a74ef5cf80f13b7.pdf dx.doi.org/10.22075/ijnaa.2018.1596.1416 Homomorphism Weak amenability of certain Banach algebras Hamid Sadeghi Department of Mathematics, Faculty of Science, University of Isfahan, Isfahan, Iran author Mahmmod Lashkarizadeh Department of Mathematics, Faculty of Science, University of Isfahan, Isfahan, Iran author text article 2018 eng In this paper we introduce the notion of $\varphi$-commutativity for a Banach algebra $A$, where $\varphi$ is a continuous homomorphism on $A$ and study the concept of $\varphi$-weak amenability for $\varphi$-commutative Banach algebras. We give an example to show that the class of $\varphi$-weakly amenable Banach algebras is larger than that of weakly amenable commutative Banach algebras. We characterize $\varphi$-weak amenability of $\varphi$-commutative Banach algebras and prove some hereditary properties. Moreover we verify some of the previous available results about commutative weakly amenable Banach algebras, for $\varphi$-commutative $\varphi$-weakly amenable Banach algebras. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 9 v. 1 no. 2018 235 245 https://ijnaa.semnan.ac.ir/article_3099_3c9686cd0612388fda1d7fbfe656ad40.pdf dx.doi.org/10.22075/ijnaa.2018.1201.1276 Higher order multi-point fractional boundary value problems with integral boundary conditions İsmail Yaslan Department of Mathematics, Science and Art Faculty, Pamukkale University, Denizli, Turkey author Mustafa Gunendi Department of Mathematics, Science and Art Faculty, Pamukkale University, Denizli, Turkey author text article 2018 eng In this paper, we concerned with positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions. We establish the criteria for the existence of at least one, two and three positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions by using a result from the theory of fixed point index, Avery-Henderson fixed point theorem and the Legget-Williams fixed point theorem, respectively. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 9 v. 1 no. 2018 247 260 https://ijnaa.semnan.ac.ir/article_3096_c23cec9aa516bada1c5c4819b2c9df69.pdf dx.doi.org/10.22075/ijnaa.2018.13610.1708