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.
Fixed point, multivalued mappings, Mizoguchi--Takahasi result, $% \theta $-contraction
MINAK, GÜLHAN and ALTUN, İSHAK
"Overall approach to Mizoguchi--Takahashi type fixed point results,"
Turkish Journal of Mathematics: Vol. 40:
4, Article 18.
Available at: https://journals.tubitak.gov.tr/math/vol40/iss4/18