A Fixed Point Theorem and Equilibria of Abstract Economies with w-Upper Semicontinuous Set-Valued Maps

TL;DR

This paper introduces new mathematical concepts of w-upper semicontinuous set-valued maps and e-USS-property, providing fixed-point theorems that lead to novel equilibrium results in abstract economies.

Contribution

It presents new fixed-point theorems based on w-upper semicontinuity and introduces the e-USS-property, advancing the theoretical framework for equilibria in abstract economies.

Findings

New fixed-point theorem for w-upper semicontinuous maps

Introduction of the e-USS-property for set-valued maps

Application to derive novel equilibrium theorems in abstract economies

Abstract

We introduce the notion of w-upper semicontinuous set valued maps and give a new fixed-point theorem. We also introduce the notion of set valued maps with e-USS-property. These results can be applied to obtain some new equilibrium theorems for abstract economies.