NEW BEST PROXIMITY POINT RESULTS FOR DIFFERENT TYPES OF NONSELF PROXIMAL CONTRACTIONS WITH AN APPLICATION

Abstract

A new variety of non-self generalized proximal contraction, called Hardy-Rogers α^+ F−proximal contraction, is shown in this work. Also, with an example, we prove that such contractions satisfying some conditions must have a unique best proximity point. For some particular values of the constants, that we have used to generalize the proximal contraction, we conclude different α^+ F−proximal contraction results of the types Ćirić, Chatterjea, Reich, Kannan, and Banach with proof, that all such type of contractions must have unique best proximity point. We also apply our result to solve a functional equation