Common fixed points of two pairs of selfmaps satisfying a contractive condition with rational expression

Abstract

In this paper, we prove the existence of common fixed points of two pairs of selfmaps under the assumptions that these two pairs of maps are weakly compatible and satisfying a contractive condition involving rational expression in a complete metric space. The same is extended to a sequence of selfmaps. Also, we prove the same with different hypotheses on two pairs of selfmaps in which one pair is compatible, reciprocally continuous and the other one is weakly compatible. We also discuss the importance of rational expression in our contractive condition. Our theorems extend the results of Chandok [1] to two pairs of selfmaps.