Kamal Fallahi - Department of Mathematics, Payam Noor University, Tehran, Iran.

In this paper‎, ‎we introduce a new type of graph contraction using a special class of functions and give a best proximity point theorem for this contraction in complete metric spaces endowed with a graph under two different conditions‎. ‎We then support our main theorem by a non-trivial example and give some consequences of best proximity point of it for usual graphs.

Best proximity point‎, ‎G-continuous mapping‎, ‎G-varphi-contraction