Relation-theoretic contraction principle

摘要

In this paper, we present yet another new and novel variant of classical Banach contraction principle on a complete metric space endowed with a binary relation which, under universal relation, reduces to Banach contraction principle. In process, we observe that various kinds of binary relations, such as partial order, preorder, transitive relation, tolerance, strict order, symmetric closure, etc., utilized by earlier authors in several well-known metrical fixed point theorems can be weakened to the extent of an arbitrary binary relation.