Condensing and Semi-continuous Multi-functions on Uniform Spaces

TL;DR

This paper extends concepts like non-compactness measure and condensing operators from metric spaces to uniform spaces, unifying classical nonlinear analysis results and applying them to locally convex spaces.

Contribution

It introduces extensions of key nonlinear analysis concepts to uniform spaces, broadening their applicability and unifying results across different topological structures.

Findings

Extended non-compactness measure to uniform spaces

Generalized condensing operators in uniform spaces

Unified results in metric and vector topological spaces

Abstract

Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in nonlinear analysis. An application of our results is given for operators defined on locally convex spaces. The main aim of this work is to unify some well-known results existing in complete metric and vector topological spaces.