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.