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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.

journal of function spaces

Periodic and Fixed Points for Caristi-Type <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mi>G</mi> </math>-Contractions in Extended <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <mi>b</mi> </math>-Gauge Spaces

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

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