Caristi-Kirk type and Boyd&Wong-Browder-Matkowski-Rus type fixed point results in b-metric spaces

TL;DR

This paper establishes new fixed point theorems in b-metric spaces, extending existing results for multi-valued operators using a key lemma on sequence Cauchy conditions.

Contribution

It introduces Caristi-Kirk and Boyd&Wong-Browder-Matkowski-Rus type fixed point results specifically in b-metric spaces, extending prior theorems from related literature.

Findings

New fixed point theorems in b-metric spaces

Extension of previous theorems from [Bota et al., 2015]

Applicable to multi-valued operators

Abstract

In this paper, based on a lemma giving a sufficient condition for a sequence with elements from a b-metric space to be Cauchy, we obtain Caristi-Kirk type and Boyd&Wong-Browder-Matkowski-Rus type fixed point results in the framework of b-metric spaces. In addition, we extend Theorems 1,2 and 3 from [M. Bota,V. Ilea, E. Karapinar, O. Mlesnite, On alpha-star-phi-contractive multi-valued operators in b-metric spaces and applications, Applied Mathematics & Information Sciences, 9 (2015), 2611-2620].