## A GENERALIZATION OF RELATION-THEORETIC CONTRACTION PRINCIPLE

## A GENERALIZATION OF RELATION-THEORETIC CONTRACTION PRINCIPLE

*D. Khantwal, S. Aneja, G. Prasad, U. C. Gairola*

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## 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 under- lying 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 â€€xed points in relational metric spaces.

## Keywords

Fixed point, Contraction mapping, Binary relation, K-continuous mapping.