Coincidence points in dislocated b-metric spaces via digraphs and L-simulation functions

Abstract

In this article, we introduce a new generalized contraction by using $\mathscr{L}$-simulation functions, $\theta$-functions and digraphs. We discuss a sufficient condition for the existence and uniqueness of points of coincidence and common fixed points for a pair of self mappings satisfying such contractions in dislocated b-metric spaces. Our main result will extend several comparable results in the existing literature. In Section 4 of this article, we exhibit that this extension is viable which will justify the new contraction.