Article

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

Published in: Quaestiones Mathematicae
Volume 43 , issue 3 , 2020 , pages: 409–424

DOI: 10.2989/16073606.2019.1578293

Author(s): Satish Shukla Department of Applied Mathematics, India , Rosana Rodríguez-López Departamento de Ańalisis Matemático, Estadística y Optimización, Facultad de Matemáticas, Spain

Keywords: 54H25 , 47H10 , 03D20 , 54H25 , 47H10 , 03D20

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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.

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