Overall approach to Mizoguchi--Takahashi type fixed point results

Authors: GÜLHAN MINAK, İSHAK ALTUN

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.

Keywords: Fixed point, multivalued mappings, Mizoguchi--Takahasi result, $% \theta $-contraction

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