Edelstein's Theorem for Cyclic Contractive Mappings in Strictly Convex Banach Spaces. (3rd July 2020)

• Record Type: Journal Article
• Authors: Gabeleh, M.; Felicit, J. Maria; Eldred, A. Anthony
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 9(2020)
• Page Start: 1027
• Page End: 1044
• Publication Date: 2020-07-03
• Subjects: Asymptotically relatively nonexpansive mapping -- best proximity point -- iterate sequence -- strictly convex Banach space; 47H10 -- 47H09 -- 46B20; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2020.1737114
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In the current paper, we discuss sufficient and necessary conditions for the existence of best proximity points for cyclic f - contractive mappings in the setting of strictly convex Banach spaces. Extensions of Edelstein's theorem are considered as well as an extension of a main result in Park [Park, S. (1978). Fixed points of f -contractive maps. Rocky Mountain J. Math . 8:743–750]. Another existence result of best proximity points will be obtained for asymptotically relatively nonexpansive mappings under different conditions with respect to the recent paper of Rajesh and Veeramani [Rajesh, S., Veeramani, P. (2016). Best Proximity point theorems for asymptotically relatively nonexpansive mappings. Numer. Funct. Anal. Optim . 37:80–91].