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...

The intent of the paper is to study semi-cyclic type contraction condition for a pair of maps (S, T). Our aim is to establish an existence theorem for common fixed points and best proximity points for such a pair in Banach spaces. The results obtained herein extend some recent results.

*Correspondence: [email protected] Department of Mathematics and Computer Science, Institut National Des Sciences Appliquée et de Technologie de Tunis, Carthage University, Centre Urbain Nord BP 676, Tunis, 1080, Tunisia Abstract Herein, we search for some best proximity point results for a novel class of non-self-mappings T : A−→ B called generalized proximal α-β-quasi-contractive. We illus...