In this paper, a common fixed point theorem for pair of weakly compatible mappings in the setting digital metric space is proved with supportive example. Our result extends and improves Ozgur Ege et al. [2].

We introduce a new pair of mappings (S,T) on D*-metric spaces called DS*-W.C. and DRS*-W.C. Many examples are presented to show the difference between these other types in literature. Moreover, we obtain several common fixed point results by using (E.A) property. then employ establish existence uniqueness solution for class nonlinear integral equations.

INTRODUCTION There have been a number of generalizations of metric spaces. One such generalization is Menger space introduced in 1942 by Menger[9] who used distribution functions instead of nonnegative real numbers as values of the metric. This space was expanded rapidly with the pioneering works of Schweizer and Sklar [11, 12]. Modifying the idea of Kramosil and Michalek [7], George and Veeram...