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

Fixexd point theory and applications

Hafiz Fukhar-ud-din¹  Muhammad Aqeel Ahmad Khan²  Amna Kalsoom³ 

[1] Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia;Department of Mathematics, COMSATS Institute of Information Technology, Lahore, Pakistan;Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, Pakistan

关键词: total asymptotically nonexpansive mapping;    common fixed point;    hyperbolic space;    modulus of uniform convexity;    asymptotic center;    47H09;    47H10;    49M05;   

DOI  :  10.1186/s13663-015-0483-2

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

This paper provides a fixed point theorem and iterative construction of a common fixed point for a general class of nonlinear mappings in the setup of uniformly convex hyperbolic spaces. We translate a multi-step iteration, essentially due to Chidume and Ofoedu (J. Math. Anal. Appl. 333:128-141, 2007) in such a setting for the approximation of common fixed points of a finite family of total asymptotically nonexpansive mappings. As a consequence, we establish strong and △-convergence results which extend and generalize various corresponding results established in the current literature.

【 授权许可】

CC BY