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 fixed 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 fixed 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.