Generalization of best proximity points theorem for non-self proximal contractions of first kind

Abstract

Abstract The primary objective of this paper is the study of the generalization of some results given by Basha (Numer. Funct. Anal. Optim. 31:569–576, 2010). We present a new theorem on the existence and uniqueness of best proximity points for proximal β-quasi-contractive mappings for non-self-mappings S:M→N $S:M\rightarrow N$ and T:N→M $T:N\rightarrow M$. Furthermore, as a consequence, we give a new result on the existence and uniqueness of a common fixed point of two self mappings.

Keywords

• Best proximity points
• Proximal β-quasi-contractive mappings on metric spaces and proximal cyclic contraction