The approximate fixed point property in Hausdorff topological vector spaces and applications

TL;DR

This paper proves an approximate fixed point theorem for self-maps on compact convex sets in Hausdorff topological vector spaces without requiring continuity, expanding fixed point theory applicability.

Contribution

It introduces an approximate fixed point result applicable to non-continuous maps in Hausdorff topological vector spaces, broadening existing fixed point theorems.

Findings

Established an approximate fixed point property for non-continuous maps.

Extended fixed point theory to broader classes of topological vector spaces.

Potential applications in nonlinear analysis and optimization.

Abstract

We establish an approximate fixed point result for self-maps on compact convex subsets of Hausdorff topological vector spaces where continuity is not a necessary condition.