On Some Fixed Point Theorems for $\mathcal{G} (\Sigma, \vartheta, \Xi )-$Contractions in Modular $b-$Metric Spaces

Abstract

This article aims to specify a new $C-$class function endows with altering distance and ultra altering distance function via generalized $\Xi -$ contraction, which is called as the $\mathcal{G}\left( {\Sigma ,\vartheta ,\Xi } \right) - $contraction in modular $b-$metric space. Regarding these new contraction type mappings, the study includes some existence and uniqueness theorems, and to indicate the usability and productivity of these results, some applications related to integral type contractions and an application to the graph structure.