Overall approach to Mizoguchi--Takahashi type fixed point results

Abstract

In this work, inspired by the recent technique of Jleli and Samet, we give a new generalization of the wellknown Mizoguchi–Takahashi fixed point theorem, which is the closest answer to Reich’s conjecture about the existence of fixed points of multivalued mappings on complete metric spaces. We also provide a nontrivial example showing that our result is a proper generalization of the Mizoguchi–Takahashi result.