Common fixed point via new type of implicit relations

Abstract

This paper focuses on three things. Firstly, we define a new type of implicit relations which covers a multitude of contractive conditions in one go. Secondly, we use this implicit relation to prove a new common fixed point theorem for four occasionally weakly biased maps of type (A) in a dislocated metric space. This theorem improves some results existing in the fixed point theory’s environment. Thirdly, we will provide an example to illustrate our main theorem and to expound the credibility and generality of our result.