Fixed points of multi-valued relation-theoretic contractions in metric spaces and application. Issue 3 (3rd March 2020) - Shukla, Satish; Rodríguez-López, Rosana
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.