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 well-known 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.