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

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