MATHEMATICAL SCIENCES
Year:2009 | Volume:3 | Issue:1|Papers Count:8

The purpose of this paper is to study the solvability for a class of generalized strong vector equilibrium-like problems in reflexive Banach spaces. Firstly, utilizing Brouwer’s fixed point theorem, we prove the solvability for this class of generalized strong vector equilibrium-like problems without monotonicity assumption. Secondly, we introduce the new concept of pseudomonotonicity for vector set-valued mapping and prove the solvability for this class of generalized strong vector equilibrium-like problems for pseudomonotone vector set-valued mapping by using Fan’s lemma and Nadler’s theorem. Our results extend and improve the corresponding results in this direction.

In this paper, we will explain how to find differential invariants of unimodular Lie group SL(2) on the space of homogeneous polynomials of degree n by Hilbert’s operators.

This paper provides necessary and sufficient conditions for Y-strong stability of the trivial solutions of homogeneous system corresponding to non-linear volterra integro-differential system. Further, sufficient conditions are also obtained for Y-strong stability of the trivial solutions of non-linear volterra integro-differential system.

In this article we obtain for the arithmetic progression of positive integers ki-r an asymptotic formula, namely Pn i=1 (ki-r) ~ arknnnn-r/k+1/2/en (k>0) (r = 0, 1, . . ., k-1), which generalizes the Stirling’s formula for the sequence i of all positive integers. In this formula ar is a positive number which depend of r for a fixed k. We also obtain some information of the product Pn i=1 pi where pi is the i-th prime number.

Many authors have introduced the concept of fuzzy metric spaces in different ways. In this paper, we get a special structure for some separable fuzzy metric and M-fuzzy metric spaces, where the metric space has been introduced by George and Veermani.

Let G be a locally compact group or a discrete group and let w be a weight function on G. We define a new convolution on the Beurling algebra L1(G, w) and show that it is also a Banach algebra with this new convolution. We show that there is a one to one correspondence between the unitary representations of G and the non-degenerate ?-representations of L1(G, w). We show that L1(G, w) is amenable if and only if G is amenable. This improves earlier results which require w to be diagonally bounded.

One of the topics of interests in data envelopment analysis (DEA) is sensitivity analysis of specific decision making unit (DMU), which is under evaluation. Changes in inputs or outputs of any DMU can alter its classification, i.e. an efficient DMU become inefficient and vise versa. In this paper, we develop a new sensitivity analysis approach for obtaining the region of efficiency of an efficient DMU. In this region changes in inputs and outputs (inputs expansion and outputs contraction) of a DMU will not alter its efficiency status.

Compactly supported quadratic semiorthogonal B-spline wavelets together with their dual wavelets are developed to approximate the solutions of Fredholm integral equations of the second kind. First, the quadratic B-spline wavelets and their properties are presented; these properties are then utilized to reduce the computation of integral equations to some algebraic equations.