A GENERALIZATION OF RELATION-THEORETIC CONTRACTION PRINCIPLE

A GENERALIZATION OF RELATION-THEORETIC CONTRACTION PRINCIPLE

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

[PDF]

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  xed points in relational metric spaces.

Keywords

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