Generalized Vector Quasi-Equilibrium Problems Involving Relaxed Continuity of the Set-Valued Maps

TL;DR

This paper investigates the existence of solutions for generalized vector quasi-equilibrium problems in Banach spaces, relaxing continuity assumptions and applying fixed-point and KKM principles to establish new equilibrium theorems.

Contribution

It introduces weaker continuity conditions for set-valued maps and develops new equilibrium existence theorems using fixed-point and KKM methods.

Findings

Existence of solutions under relaxed continuity assumptions

New equilibrium theorems derived from fixed-point and KKM principles

Applicability to Banach spaces

Abstract

In this paper, we study the existence of solutions for generalized vector quasi-equilibrium problems. Firstly, we prove that in the case of Banach spaces, the assumptions of continuity over correspondences can be weakened. The theoretical analysis is based on fixed-point theorems. Secondly, we establish new equilibrium theorems as applications of the KKM principle.