A Relation-Theoretic Formulation of Browder–Göhde Fixed Point Theorem

Abstract

In this paper, we introduce the concept of R-nonexpansive self-mappings defined on a suitable subset K of a Banach space, wherein R stands for a transitive binary relation on K, and utilize the same to prove a relation-theoretic variant of classical Browder–Göhde fixed point theorem. As consequences of our newly proved results, we are able to derive several core fixed-point theorems existing in the literature.

Keywords

• binary relation
• R -nonexpansive mappings%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <named-content content-type="inline-formula"><inline-formula> <mml:math id="mm5636" display="block"> <mml:semantics> <mml:mi mathvariant="script">R</mml:mi> </mml:semantics> </mml:math> </inline-formula></named-content>-nonexpansive mappings
• uniformly convex banach space
• R -intervals%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <named-content content-type="inline-formula"><inline-formula> <mml:math id="mm5637" display="block"> <mml:semantics> <mml:mi mathvariant="script">R</mml:mi> </mml:semantics> </mml:math> </inline-formula></named-content>-intervals