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.

*Correspondence: [email protected] 2Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia Full list of author information is available at the end of the article Abstract Given a non-self mapping from A to B, where A and B are subsets of a metric space, in order to compute an optimal approximate solution of the equation Sx = x, a best proximit...