Coupled common best proximity point theorems for nonlinear contractions in partially ordered metric spaces

Abstract

In this paper, we first introduce the concept of mixed γ-proximally monotone property type mappings and investigate the existence of the coupled proximally coincidence point for such mappings in partially ordered complete metric spaces. Furthermore, we prove the existence and uniqueness of coupled common best proximity points. Our results extend, improve and generalize several known results in the literature.

Keywords

• p-property
• coupled coincidence point
• coupled fixed point
• coupled common fixed point
• partially ordered set
• mixed monotone mapping