Some new coincidence point results with an application in integral equations

Abstract

In this paper, we introduce a new generalized contraction by using $\mathscr{L}$-simulation functions, $\theta$-functions and $\alpha$-admissible mappings and utilize the same to obtain a sufficient condition for the existence and uniqueness of points of coincidence and common fixed points for a pair of self mappings in dislocated $b$-metric spaces. Our main result will extend and unify several relevant results in the existing literature. We provide an application to obtain a unique solution of an integral equation.