Fixed-Point Theorems for Generalized Nonexpansive Mappings. (11th June 2019)

• Record Type: Journal Article
• Authors: Kar, Samir; Veeramani, P.
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 8(2019)
• Page Start: 888
• Page End: 901
• Publication Date: 2019-06-11
• Subjects: Asymptotic nonexpansive -- fixed point -- nonexpansive -- quasiorder relation -- uniformly convex Banach space; Primary: 47H10 -- Secondary: 46B20; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1564327
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: Using the concept of asymptotic center we obtain the existence of fixed points having preassigned location for a wider class of asymptotic nonexpansive mappings in a uniformly convex Banach space. This generalization leads us to get a recent result of Alfuraidan and Khamsi for continuous monotone asymptotic nonexpansive mappings as well as the classical fixed-point result of Geobel and Kirk for asymptotic nonexpansive mappings in a uniformly convex Banach space. Also we prove a fixed-point theorem for order preserving continuous maps on a quasiordered closed convex subset of a uniformly convex Banach sapce having monotone norm.