A generalization of relation-theoretic contraction principle

Abstract

In the present paper, we generalize relation-theoretic contraction principle using weaker class of contraction mappings which is assumed to be hold on the elements of a particular subset of the whole space, whose elements are relaxed under the underlying relation. We also relaxed the assumption of continuity from the main result of Alam and Imdad by introducing the notion of (R, k)-continuity. Moreover, our results do not require the underlying binary relation to be T-closed for existence of fixed points in relational metric spaces.