Abstract
Iterative schemas are ubiquitous in the area of abstract nonlinear analysis and still remain as a main tool for approximation of fixed points of generalizations of nonexpansive maps. The analysis of general iterative schemas, in a more general setup, is a problem of interest in theoretical numerical analysis. Therefore, we propose and analyze a general iterative schema for two finite families of asymptotically quasi-nonexpansive maps in hyperbolic spaces. Results concerning Δ-convergence as well as strong convergence of the proposed iteration are proved. It is instructive to compare the proposed general iteration schema and the consequent convergence results with that of several recent results in CAT(0) spaces and uniformly convex Banach spaces.
| Original language | English |
|---|---|
| Article number | 238 |
| Journal | Fixed Point Theory and Algorithms for Sciences and Engineering |
| Volume | 2013 |
| DOIs | |
| State | Published - Oct 2013 |
Bibliographical note
Funding Information:The authors are very grateful to the editor and anonymous referees for their helpful comments. We are indebted to Prof. Dr. Ulrich Kohlenbach for various constructive comments to improve the content of the manuscript. The author H. Fukhar-ud-din is grateful to King Fahd University of Petroleum & Minerals for supporting the research project IN 121023. The author M.A.A. Khan gratefully acknowledges the support of Higher Education Commission of Pakistan.
Keywords
- Asymptotic regularity
- Common fixed point
- General iteration schema
- Hyperbolic space
- Rates of metastability
- Weakly asymptotically quasi-nonexpansive
- Δ-convergence
ASJC Scopus subject areas
- Geometry and Topology
- Applied Mathematics