Existence results for nonexpansive multi-valued operators and nonlinear integral inclusions

TL;DR

This paper develops new fixed point theorems for countably nonexpansive multi-valued mappings in Banach algebras and applies these results to establish existence theorems for nonlinear integral and differential inclusions.

Contribution

It introduces novel fixed point theorems for multi-valued mappings and extends their application to nonlinear integral and differential inclusions.

Findings

New fixed point theorems for countably nonexpansive multi-valued mappings.

Existence results for nonlinear functional integral inclusions.

Existence results for nonlinear differential inclusions.

Abstract

In this paper, we establish some new variants of fixed point theorems for a large class of countably nonexpansive multi-valued mappings. Some fixed point theorems for the sum and the product of three multi-valued mappings defined on nonempty, closed convex set of Banach algebras are also presented. These results improve and complement a number of earlier works. As an application, we prove existence results for a broad class of nonlinear functional integral inclusions as well as nonlinear differential inclusions.