2024/05/04 by Aftab Alam, Alam, Aftab
Computer Science · #30L99 #41A65 #47H09 #47J20 #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2405.02635
openalex publication_date 2024/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce the notions of proximally completeness, proximally closedness and proximally continuity and utilize the same to prove a result on existence and uniqueness of best proximity points in the setting of metric space (not necessarily complete). Our newly proved result enriches, sharpens, improves and modifies the proximal contraction principle of Basha [J. Optim. Theory Appl. 2011:151 (2011), 210-216]. In order to illustrate the effectiveness of our finding, we discuss the sufficient conditions ensuring the existence of a unique solution of certain variational inequality problem.