Best proximity point theorems for G-proximageneralizedcontraction in complete metric spaces endowed with graphs

Abstract

© 2017 by the Mathematical Association of Thailand. All rights reserved. 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.