Best Proximity Point Theorems for G-Proximal Generalized Contraction in Complete Metric Spaces endowed with Graphs

Chalongchai Klanarong, Suthep Suantai

Abstract

In this work, we present the notion of a G-proximal generalized
contraction which is a development of well known mappings by Banach,
Kannan, Chatterjea from self mappings to non-self mappings and we
prove best proximity point theorems for this mapping in a complete
metric space endowed with a directed graph. Moreover, we apply our
main theorems to prove an existence of coupled best proximity points
in a complete metric space endowed with a directed graph.