Weak conditions for random fixed point and approximation results

TL;DR

This paper investigates conditions under which random fixed points and approximations exist for certain classes of operators in finite-dimensional Banach spaces, extending and improving existing theoretical results.

Contribution

It introduces weaker conditions for the existence of random fixed points and approximations for almost lower semicontinuous, condensing, or 1-set-contractive operators.

Findings

Established existence of random fixed points under weaker conditions.

Extended previous results to broader classes of operators.

Improved theoretical understanding of random approximations in Banach spaces.

Abstract

In this paper, we study the existence of the random approximations and fixed points for random almost lower semicontinuous operators defined on finite dimensional Banach spaces, which in addition, are condensing or 1-set-contractive. Our results either extend or improve corresponding ones present in literature.