Common fixed points of generalized contraction maps in metric spaces

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. 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. Further, we prove the same with different hypotheses on two pairs of selfmaps in which either one of the pair satisfies the property (E.A) and restricting the completeness of X to its subspace. We provide examples in support of our results.