On Proximal contractions via implicit relations and Best proximity points

[摘要] In this paper, we employ two types of implicit relations to define some new kind of proximal contractions and study about their best proximity points. More precisely, we use two class of functions A and A ′ to explore proximal A, A ′ -contractions of first and second kind and strong proximal A, A ′ -contractions. We investigate the existence of best proximity points results of the same. It is worth mentioning that the well-known results of Sadiq Basha [J. Approx. Theory, 2011] on proximal contractions are the special cases of our obtained results. We authenticate our results by suitable examples. Finally, we point out some areas where our obtained results can be applied.

[学科分类] 数学（综合）

[关键词] Best proximity point;proximal contraction;strong proximal contraction;approximative compactness.