Best proximity points of contractive mappings on a metric space with a graph and applications

Abstract

We establish an existence and uniqueness theorem on best proximity point for contractive mappings on a metric space endowed with a graph. As an application of this theorem, we obtain a result on the existence of unique best proximity point for uniformly locally contractive mappings. Moreover, our theorem subsumes and generalizes many recent fixed point and best proximity point results.

Keywords

• Fixed point
• best proximity point
• contraction
• graph
• metric space
• P-property.