Fixed points of multi-valued relation-theoretic contractions in metric spaces and application

Abstract

In this paper, we establish a relation-theoretic version of a famous xed point result of Nadler on complete metric spaces endowed with a binary  relation. Our results extend and generalize the recent result of A. Alam and M. Imdad (see [1], Relation-theoretic contraction principle, J. Fixed Point Theory Appl. 17(4) (2015), 693{702) and several other xed point results on spaces endowed with various kinds of binary relations to their multi-valued versions with weaker requirements. An application of the obtained result to the problem of existence of solution of differential inclusions is presented.

Key words: Multi-valued mapping, Hausdorff metric, xed point, binary relation.