Fixed points of multi-valued relation-theoretic contractions in metric spaces and application. Issue 3 (3rd March 2020)

• Record Type: Journal Article
• Authors: Shukla, Satish; Rodríguez-López, Rosana
• Is Part Of: Quaestiones mathematicae. Volume 43:Issue 3(2020)
• Page Start: 409
• Page End: 424
• Publication Date: 2020-03-03
• Subjects: 54H25 -- 47H10 -- 03D20; Multi-valued mapping -- Hausdorff metric -- fixed point -- binary relation; Mathematics -- Periodicals; 510.5
• DOI: 10.2989/16073606.2019.1578293
• Languages: English
• ISSNs: 1607-3606

Abstract

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.