Existence Result of Generalized Vector Quasiequilibrium Problems in Locally G-Convex Spaces

Somyot Plubtieng,Kanokwan Sitthithakerngkiet

doi:10.1155/2011/967515

Somyot Plubtieng, Kanokwan Sitthithakerngkiet

Open Access

https://doi.org/10.1155/2011/967515

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Journal: Fixed Point Theory and Applications	Publication Date: Jan 1, 2011
Citations: 3	License type: cc-by

Affiliation: Naresuan University

Abstract

This paper deals with the generalized strong vector quasiequilibrium problems without convexity in locally -convex spaces. Using the Kakutani-Fan-Glicksberg fixed point theorem for upper semicontinuous set-valued mapping with nonempty closed acyclic values, the existence theorems for them are established. Moreover, we also discuss the closedness of strong solution set for the generalized strong vector quasiequilibrium problems.

Highlights

Let X be real topological vector space, and let C be a nonempty closed convex subset of X
The main motivation of this paper is to prove the existence theorems of the generalized strong vector quasiequilibrium problems in locally G-convex spaces, by using Kakutani-Fan-Glicksberg fixed point theorem for upper semicontinuous set-valued mapping with nonempty closed acyclic values, and the closedness of Vs F and Vw F
We apply the Kakutani-Fan-Glicksberg fixed point theorem for upper semicontinuous set-valued mapping with nonempty closed acyclic values to establish two existence theorems of strong solutions and obtain the closedness of the strong solutions set for generalized strong vector quasiequilibrium problem

Summary

Introduction

Let X be real topological vector space, and let C be a nonempty closed convex subset of X. Throughout this paper, motivated and inspired by Hou et al 27 , Long et al 16 , and Yuan 28 , we will introduce and study the generalized vector quasiequilibrium problem on locally G-convex Hausdorff topological vector spaces. Let X, Y , and Z be real locally Gconvex Hausdorff topological vector spaces, K ⊂ X and D ⊂ Y nonempty compact subsets, and C ⊂ Z a nonempty closed convex cone. The main motivation of this paper is to prove the existence theorems of the generalized strong vector quasiequilibrium problems in locally G-convex spaces, by using Kakutani-Fan-Glicksberg fixed point theorem for upper semicontinuous set-valued mapping with nonempty closed acyclic values, and the closedness of Vs F and Vw F. The results in this paper generalize, extend, and unify some well-known some existence theorems in the literature

Preliminaries

Main Results

Stability