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.

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The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

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