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.