2020/08/22 by Pratikshan Mondal, Mondal, Pratikshan, Hiranmoy Garai +3
Mathematics · #47H10 #54H25 #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA)
paper · pdf · doi:10.48550/arxiv.2008.09737
openalex publication_date 2020/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 type and strong proximal A, A'-contractions. We investigate the existence of best proximity point 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.