Common best proximity point theorems for proximally weak reciprocal continuous mappings

Abstract

The main objective of this paper is to find sufficient conditions for the existence and uniqueness of common best proximity points for discontinuous non-self mappings in the setting of a complete metric space. We introduce and analyze new concepts such as proximally reciprocal continuous, proximally weak reciprocal continuous, R-proximally weak commuting of types $ M_{\Lambda} $ and $ M_{\Gamma} $ for non-self mappings. Furthermore, we obtain a common best proximity point theorem for such mappings. In addition, we provide an example to support our main result.

Keywords

• compatible mappings
• weak reciprocal continuity
• r-weakly commuting of type $ m_{\lambda} $ and $ m_{\gamma} $