On Common fixed point results via implicit relations

Abstract

. There are certain contractive conditions (and contractions) available in the literature that ensure the existence of common fixed points of a couple and a family of mappings. However, to verify the validity of these conditions, each result must be checked separately. Thus, it becomes legitimate to obtain some contraction or contractive conditions that can bypass the computational difficulties of checking contraction and contractive conditions via individual res-ults and ensure the existence of common fixed points simultaneously. In this article, by the virtue of implicit relations, we acquire some contraction and contractive conditions, christened A -contraction and A -contractive conditions, which serve the desired purpose. The utility of the established conditions is exhibited through some typical fixed point results and concrete examples.