Mann iteration process for asymptotic pointwise nonexpansive mappings in metric spaces

被引：21

作者：

Ibn Dehaish, B. A. ^{[2
]}

Khamsi, M. A. ^{[1
]}

Khan, A. R. ^{[3
]}

机构：

[1] Univ Texas El Paso, Dept Math Sci, El Paso, TX 79968 USA

[2] King Abdulaziz Univ, Fac Sci Girls, Dept Math, Jeddah 21593, Saudi Arabia

[3] King Fahd Univ Petr & Minerals, Dept Math & Stat, Dhahran 31261, Saudi Arabia

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2013年 / 397卷 / 02期

关键词：

Asymptotically nonexpansive mapping; Asymptotic pointwise nonexpansive mapping; Fixed point; Inequality of Bruhat and Tits; Mann iteration process; Uniformly convex metric space; Uniformly Lipschitzian mapping; FIXED-POINTS; INEQUALITIES;

D O I：

10.1016/j.jmaa.2012.08.013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let (M, d) be a complete 2-uniformly convex metric space. Let C be a nonempty, bounded, closed, and convex subset of M, and let T : C -> C be an asymptotic pointwise nonexpansive mapping. In this paper, we prove that the modified Mann iteration process defined by Xn+1 = t(n)T(n) (x(n)) circle plus (1 - t(n))x(n) converges in a weaker sense to a fixed point of T. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：861 / 868

页数：8

共 22 条

[1]

[Anonymous], 1999, METRIC SPACES NONPOS

[2]

Beauzamy B., 1985, Introduction to Banach Spaces and Their Geometry

[3]

Bruhat F., 1972, Publications Mathematiques, V41, P5

[4] SPACES WITH NON-POSITIVE CURVATURE [J].

BUSEMANN, H .

ACTA MATHEMATICA, 1948, 80 (04) :259-310

[5]

Goebel K., 1984, SERIES MONOGRAPHS TX, V83

[6] Applications of the best approximation operator to *-nonexpansive maps in Hilbert spaces [J].

Hussain, N ;

Khan, AR .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2003, 24 (3-4) :327-338

[7] On asymptotic pointwise contractions in metric spaces [J].

Hussain, N. ;

Khamsi, M. A. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (10) :4423-4429

[8] Inequalities in metric spaces with applications [J].

Khamsi, M. A. ;

Khan, A. R. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (12) :4036-4045

[9]

Khamsi M.A., 2001, An Introduction to Metric Spaces and Fixed Point Theory

[10] Strong convergence of a general iteration scheme in CAT(0) spaces [J].

Khan, Abdul Rahim ;

Khamsi, Mohamed Amine ;

Fukhar-ud-Din, Hafiz .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (03) :783-791

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