Best proximity point for different types ofnon-self proximal contractions

Abstract

A new variety of non-self generalised poximal contraction,called Hardy-Rogers α+F-proximal contraction, is shown in this work.Also we have proved that such contractions satisfying some conditionsmust have unique best proximity point. For some particular values of theconstants, that we have used to generalize the proximal contraction, weconclude different α+F-proximal contraction results of the types ´Ciri´c,Chatterjea, Reich, Kannan and Banach with proof, that all such typeof contractions must have unique best proximity point.