The Stability and Well-Posedness of Fixed Points for Relation-Theoretic Multi-Valued Maps

Isaac Karabo Letlhage, Deepak Khantwal, Rajendra Pant and Manuel De la Sen ()
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Isaac Karabo Letlhage: Department of Mathematics and Applied Mathematics, University of Johannesburg, Kingsway Campus, Auckland Park 2006, South Africa
Deepak Khantwal: Department of Mathematics and Applied Mathematics, University of Johannesburg, Kingsway Campus, Auckland Park 2006, South Africa
Rajendra Pant: Department of Mathematics and Applied Mathematics, University of Johannesburg, Kingsway Campus, Auckland Park 2006, South Africa
Manuel De la Sen: Institute of Research and Development of Processes IIDP, Faculty of Science and Technology, University of the Basque Country, de Bilbao, Barrio Sarriena, 48940 Leioa, Bizkaia, Spain

Mathematics, 2023, vol. 11, issue 20, 1-13

Abstract: The purpose of this study is to present fixed-point results for Suzuki-type multi-valued maps using relation theory. We examine a range of implications that arise from our primary discovery. Furthermore, we present two substantial cases that illustrate the importance of our main theorem. In addition, we examine the stability of fixed-point sets for multi-valued maps and the concept of well-posedness. We present an application to a specific functional equation which arises in dynamic programming.

Keywords: metric space; binary relation; relation-theoretic contraction; fixed points (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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