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

Abstract

The study of fixed point theory combining digraphs and L-simulation functions is a new development in the domain of contractive type single valued theory. In this paper, we introduce the notion of a generalized LG- contraction by using L-simulation functions and digraphs. We discuss the existence and uniqueness of points of coincidence and common fixed points for a pair of self-mappings satisfying such contractions in bmetric spaces. Our result will extend and unify several comparable results in the existing literature including the well known Banach contraction theorem in metric spaces. Finally, we give some non-trivial examples to illustrate and justify the validity of our main result.