Periodic and Fixed Points for Caristi-Type G -Contractions in Extended b -Gauge Spaces

Abstract

In this paper, we introduce extended $b$ -gauge spaces and the extended family of generalized extended pseudo- $b$ -distances. Moreover, we define the sequential completeness and construct the Caristi-type $G$ -contractions in the framework of extended $b$ -gauge spaces. Furthermore, we develop periodic and fixed point results in this new setting endowed with a graph. The obtained results of this paper not only generalize but also unify and improve the existing results in the corresponding literature.