Sahand Communications in Mathematical Analysis
Volume:3 Issue: 2, Winter-Spring 2016

In 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, R0, is derived. The results show that the dynamics of the model is completely determined by the basic reproductive number R0. If R01 , the disease-free equilibrium is unstable and the disease is uniformly persistent.

In 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.

In 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.

The 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 F3[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.

The 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.

In this paper, we study the Arens regularity properties of module actions. We investigate some properties of topological centers of module actions ZℓB∗∗(A∗∗) and ZℓA∗∗(B∗∗) with some conclusions in group algebras.

In this manuscript, we study the inverse problem for non self-adjoint Sturm--Liouville operator −D2 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.

In this paper, we study some kinds of majorizations on Mn 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 Φ with the property Φ(AB)=Φ(A)Φ(B) for every A,B∈Mn.

In this article, the notion of n−derivation is introduced for all integers n≥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.