2023/10/16 by Abhik Digar, Digar, Abhik
Mathematics · #46C20 #47H10 #54H25 #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA)
paper · pdf · doi:10.48550/arxiv.2310.10154
openalex publication_date 2023/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we introduce a geometrical notion, property strongly UC which is stronger than property UC and prove the existence of best approximations for a new class of almost cyclic ψ-contraction maps in a metric space. As a particular case, we obtain the main results of [Sadiq Basha, S., Best approximation theorems for almost cyclic contractions. J. Fixed Point Theory Appl. 23 (2021), MR4254305] and [Eldred, A. Anthony; Veeramani, P., Existence and convergence of best proximity points. J. Math. Anal. Appl. 323 (2006), MR2260159]. Moreover, we study the existence of best approximations for almost cyclic contractions in a reflexive Banach space.