An integral Suzuki-type fixed point theorem with application

TL;DR

This paper introduces a new fixed point theorem for multivalued mappings using integral contractions and applies it to ensure solutions exist and are unique for certain functional equations in dynamic programming.

Contribution

It presents a novel integral Suzuki-type fixed point theorem for multivalued mappings and demonstrates its application in solving functional equations in dynamic programming.

Findings

Established an integral Suzuki-type fixed point theorem for multivalued mappings.

Proved existence and uniqueness of solutions for a class of functional equations in dynamic programming.

Abstract

In this paper, we present an integral Suzuki-type fixed point theorem for multivalued mappings defined on a complete metric space in terms of the \'{C}iri\'{c} integral contractions. As an application, we will prove an existence and uniqueness theorem for a functional equation arising in dynamic programming of continuous multistage decision processes.