Sahand Communications in Mathematical Analysis
Volume:3 Issue: 1, Winter-Spring 2016

Abstract. The purpose of the present study is to introduce the sequence space lp(E,∆) = x = (xn)∞ n=1: ∞ ∑ n=1   ∑j ∈En xj − ∑ j∈En+1 xj  p < ∞, where E = (En) is a partition of finite subsets of the positive integers and p ≥ 1. The topological properties and inclusion relations of this space are studied. Moreover, the problem of finding the norm of certain matrix operators such as Copson and Hilbert from lp into lp(E,∆) is investigated.

In this paper, we apply the local fractional Adomian decomposition and variational iteration methods to obtain the analytic approximate solutions of Fredholm integral equations of the second kind within local fractional derivative operators. The iteration procedure is based on local fractional derivative. The obtained results reveal that the proposed methods are very efficient and simple tools for solving local fractional integral equations.

In the mathematical analysis, there are some theorems and definitions that established for both real and fuzzy numbers. In this study, we try to prove Bernoulli's inequality in fuzzy real numbers with some of its applications. Also, we prove two other theorems in fuzzy real numbers which are proved before, for real numbers.

For entire functions, the notions of their growth indicators such as Ritt order are classical in complex analysis. But the concepts of relative Ritt order of entire functions and as well as their technical advantages of not comparing with the growths of expexpz exp⁡exp⁡z are not at all known to the researchers of this area. Therefore the studies of the growths of entire functions in the light of their relative Ritt order are the prime concern of this paper. Actually in this paper we establish some newly developed results related to the growth rates of entire functions on the basis of their relative Ritt order (respectively, relative Ritt lower order).

In this study, the Bernoulli polynomials are used to obtain an approximate solution of a class of nonlinear two-dimensional integral equations. To this aim, the operational matrices of integration and the product for Bernoulli polynomials are derived and utilized to reduce the considered problem to a system of nonlinear algebraic equations. Some examples are presented to illustrate the efficiency and accuracy of the method.

Abstract. In this paper, we give a characterization of strongly Jordan zero-product preserving maps on normed algebras as a generalization of Jordan zero-product preserving maps. In this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly Jordan zero-product preserving maps are completely different. Also, we prove that the direct product and the composition of two strongly Jordan zero-product preserving maps are again strongly Jordan zero-product preserving maps. But this fact is not the case for tensor product of them in general. Finally, we prove that every ∗−preserving linear map from a normed∗−algebra into a C∗−algebra that strongly preserves Jordan zero-products is necessarily continuous.

Abstract. Let f be a locally univalent function on the unit disk U. We consider the normalized extensions of f to the Euclidean unit ball Bn ⊆Cn given by Φn,γ(f)(z) =(f(z1),(f′(z1))γ ˆ z),where γ ∈ [0,1/2], z = (z1, ˆ z) ∈ Bn and Ψn,β(f)(z) =(f(z1),(f(z1) z1)β ˆ z), in which β ∈ [0,1], f(z1) ̸= 0 and z = (z1, ˆ z) ∈ Bn. In the case γ = 1/2, the function Φn,γ(f) reduces to the well known Roper-Suffridge extension operator. By using different methods, we prove that if f is parabolic starlike mapping on U then Φn,γ(f) and Ψn,β(f) are parabolic starlike mappings on Bn.