Existence and higher arity iteration for total asymptotically\n nonexpansive mappings in uniformly convex hyperbolic spaces

2013/12/09 by Hafiz Fukhar-ud-din, Fukhar-ud-din, Hafiz, Amna Kalsoom +3
Computer Science · Mathematics · #47H09 #47H10 #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #Optimization and Variational Analysis #Secondary: 49M05

paper · pdf · doi:10.48550/arxiv.1312.2418

openalex publication_date 2013/12/09 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

This paper provides a fixed point theorem and iterative construction of a\ncommon fixed point for a general class of nonlinear mappings in the setup of\nuniformly convex hyperbolic spaces. We translate a multi-step iteration,\nessentially due to Chidume and Ofoedu [4] in such setting for the approximation\nof common fixed points of a finite family of total asymptotically nonexpansive\nmappings. As a consequence, we establish strong and del-convergence results\nwhich extend and generalize various corresponding results announced in the\ncurrent literature.\n

Citations

• Nonexpansive iterations in uniformly convex W-hyperbolic spaces

Related

• Asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces
• Construction of fixed points of asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces
• On unification of the strong convergence theorems for a finite family of\n total asymptotically nonexpansive mappings in Banach spaces
• Approximating fixed points of asymptotically nonexpansive mappings in\n Banach spaces by metric projections
• Weak and strong convergence to fixed points of asymptotically nonexpansive mappings