A Study on (?,?) Weakly Contractive Mapping via (F,h) Upper Class

Abstract

Branciari reorganized the notion of metric to attain a novel distance function by replacing the triangular inequality with the quadrilateral inequality. The reorganized metric function was said rectangular metric in some resources, or general metric in some others. Ansari introduced a more general function so-called upper class. Inspired and motivated by this facts, we give an extansion of weakly contractive mapping via upper class type II in the setting of Branciari metric space. An application is given here to prove new fixed point results for graphic weakly contractive mappings in Branciari metric space endowed with a graph. Moreover, we derive an example in support of our main results.