Common Fixed Points Via R-Functions and Digraphs with an Application to Homotopy Theory

The basic purpose of this article is to introduce the concept of R − λ − G-contraction by using R-functions, lower semi-continuous functions and digraphs and discuss the existence and uniqueness of points of coincidence and common fixed points for a pair of self-mappings satisfying such contractions in the setting of metric spaces endowed with a graph. As some consequences of our results, we obtain several recent results in metric spaces and partial metric spaces.