Edelstein's Theorem for Cyclic Contractive Mappings in Strictly Convex Banach Spaces. (3rd July 2020) - Gabeleh, M.; Felicit, J. Maria; Eldred, A. Anthony
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].