University of MaraghehSahand Communications in Mathematical Analysis2322-580703220160601The analysis of a disease-free equilibrium of Hepatitis B model11119749ENReza AkbariDepartment of Mathematical Sciences, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran.Ali Vahidian KamyadDepartment of Mathematics Sciences, University of Ferdowsi, Mashhad, Iran.Ali akbar HeydariResearch Center for Infection Control and Hand Hygiene, Mashhad University Of Medical Sciences, Mashhad, Iran.Aghileh HeydariDepartment of Mathematical Sciences, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran.Journal Article20150921In this paper we study the dynamics of Hepatitis B virus (HBV) infection under administration of a vaccine and treatment, where the disease is transmitted directly from the parents to the offspring and also through contact with infective individuals. Stability of the disease-free steady state is investigated. The basic reproductive rate, $R_0$, is derived. The results show that the dynamics of the model is completely determined by the basic reproductive number $R_0$. If $R_0<1$, the disease-free equilibrium is globally stable and the disease always dies out and if $R_0>1$, the disease-free equilibrium is unstable and the disease is uniformly persistent.University of MaraghehSahand Communications in Mathematical Analysis2322-580703220160601Growth analysis of entire functions of two complex variables132419750ENSanjib Kumar DattaDepartment of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN-741235, West Bengal, India.Tanmay BiswasRajbari, Rabindrapalli, R. N. Tagore Road, P.O.-Krishnagar, Dist-Nadia, PIN-741101, West Bengal, India.Journal Article20151115In this paper, we introduce the idea of generalized relative order (respectively generalized relative lower order) of entire functions of two complex variables. Hence, we study some growth properties of entire functions of two complex variables on the basis of the definition of generalized relative order and generalized relative lower order of entire functions of two complex variables.University of MaraghehSahand Communications in Mathematical Analysis2322-580703220160601Menger probabilistic normed space is a category topological vector space253219784ENIldar SadeqiDepartment of Mathematics, Faculty of Science, Sahand University of Technology, Tabriz, Iran.Farnaz Yaqub AzariUniversity of Payame noor, Tabriz, Iran.Journal Article20150419In this paper, we formalize the Menger probabilistic normed space as a category in which its objects are the Menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. Then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. So, we can easily apply the results of topological vector spaces in probabilistic normed spaces.University of MaraghehSahand Communications in Mathematical Analysis2322-580703220160601On certain fractional calculus operators involving generalized Mittag-Leffler function334519751ENDinesh KumarDepartment of Mathematics \& Statistics, Jai Narain Vyas University, Jodhpur - 342005, India.Journal Article20160104The object of this paper is to establish certain generalized fractional integration and differentiation involving generalized Mittag-Leffler function defined by Salim and Faraj [25]. The considered generalized fractional calculus operators contain the Appell's function $F_3$ [2, p.224] as kernel and are introduced by Saigo and Maeda [23]. The Marichev-Saigo-Maeda fractional calculus operators are the generalization of the Saigo fractional calculus operators. The established results provide extensions of the results given by Gupta and Parihar [3], Saxena and Saigo [30], Samko et al. [26]. On account of the general nature of the generalized Mittag-Leffler function and generalized Wright function, a number of known results can be easily found as special cases of our main results.University of MaraghehSahand Communications in Mathematical Analysis2322-580703220160601Multistep collocation method for nonlinear delay integral equations476519832ENParviz DaraniaDepartment of Mathematics, Faculty of Science, Urmia University, P.O.Box 5756151818, Urmia-Iran.Journal Article20150720The main purpose of this paper is to study the numerical solution of nonlinear Volterra integral equations with constant delays, based on the multistep collocation method. These methods for approximating the solution in each subinterval are obtained by fixed number of previous steps and fixed number of collocation points in current and next subintervals. Also, we analyze the convergence of the multistep collocation method when used to approximate smooth solutions of delay integral equations. Finally, numerical results are given showing a marked improvement in comparison with exact solution.University of MaraghehSahand Communications in Mathematical Analysis2322-580703220160601On the topological centers of module actions677419748ENKazem Haghnejad AzarDepartment of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran.Journal Article20150418In this paper, we study the Arens regularity properties of module actions. We investigate some properties of topological centers of module actions ${Z}^ell_{B^{**}}(A^{**})$ and ${Z}^ell_{A^{**}}(B^{**})$ with some conclusions in group algebras.University of MaraghehSahand Communications in Mathematical Analysis2322-580703220160601Inverse Sturm-Liouville problems with a Spectral Parameter in the Boundary and transmission conditions758917973ENMohammad ShahriariDepartment of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran.Journal Article20150512In this manuscript, we study the inverse problem for non self-adjoint Sturm--Liouville operator $-D^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. By defining a new Hilbert space and using its spectral data of a kind, it is shown that the potential function can be uniquely determined by part of a set of values of eigenfunctions at some interior point and parts of two sets of eigenvalues.University of MaraghehSahand Communications in Mathematical Analysis2322-580703220160601On multiplicative (strong) linear preservers of majorizations9110618507ENMohammad Ali Hadian NadoshanDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Zip Code: 7718897111, Rafsanjan, Iran.Ali ArmandnejadDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Zip Code: 7718897111, Rafsanjan, Iran.Journal Article20151224In this paper, we study some kinds of majorizations on $textbf{M}_{n}$ and their linear or strong linear preservers. Also, we find the structure of linear or strong linear preservers which are multiplicative, i.e. linear or strong linear preservers like $Phi $ with the property $Phi (AB)=Phi (A)Phi (B)$ for every $A,Bin textbf{M}_{n}$.University of MaraghehSahand Communications in Mathematical Analysis2322-580703220160601On $n$-derivations10711519780ENMohammad Hossein SattariDepartment of Mathematics, Faculty of Science, Azarbaijan Shahid Madani University, P.O.Box 53751-71379, Tabriz, Iran.Journal Article20160225In this article, the notion of $n-$derivation is introduced for all integers $ngeq 2$. Although all derivations are $n-$derivations, in general these notions are not equivalent. Some properties of ordinary derivations are investigated for $n-$derivations. Also, we show that under certain mild condition $n-$derivations are derivations.