Periodic and fixed points for Caristi-type \(G\)-contractions in extended \(b\)-gauge spaces (Q2050369)

Summary: 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.