An implicit algorithm for two finite families of nonexpansive maps in hyperbolic spaces

被引：96

作者：

Khan, Abdul Rahim ^{[1
]}

Fukhar-ud-din, Hafiz ^{[1
,2
]}

Khan, Muhammad Aqeel Ahmad ^{[2
]}

机构：

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

[2] Islamia Univ Bahawalpur, Dept Math, Bahawalpur 63100, Pakistan

来源：

FIXED POINT THEORY AND APPLICATIONS | 2012年

关键词：

hyperbolic space; nonexpansive map; common fixed point; implicit algorithm; condition(A); semi-compactness; Delta-convergence; FIXED-POINTS; STRONG-CONVERGENCE; ITERATIONS;

D O I：

10.1186/1687-1812-2012-54

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we propose and analyze an implicit algorithm for two finite families of nonexpansive maps in hyperbolic spaces. Results concerning Delta-convergence as well as strong convergence of the proposed algorithm are proved. Our results are refinement and generalization of several recent results in CAT(0) spaces and uniformly convex Banach spaces. Mathematics Subject Classification (2010): Primary: 47H09; 47H10; Secondary: 49M05.

引用

页码：1 / 12

页数：12

共 26 条

[1]

Bauschke HH, 2011, CMS BOOKS MATH, P1, DOI 10.1007/978-1-4419-9467-7

[2]

Bose S C., 1985, J. Math. Phys. Sci, V19, P503

[3] An example on the Mann iteration method for Lipschitz pseudocontractions [J].

Chidume, CE ;

Mutangadura, SA .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 129 (08) :2359-2363

[4] On Δ-convergence theorems in CAT(0) spaces [J].

Dhompongsa, S. ;

Panyanak, B. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 56 (10) :2572-2579

[5]

Fukhar-ud-din H., 2005, Int. J. Math. Math. Sci, V10, P1643, DOI [10.1155/IJMMS.2005.1643, DOI 10.1155/IJMMS.2005.1643]

[6]

Goebel K, 1984, Uniform convexity, hyperbolic geometry, and non-expansive mappings

[7]

Goebel K., 1983, American Mathematical Society, Providence, RI ppMathematics, V21, P115

[8] FIXED-POINTS BY A NEW ITERATION METHOD [J].

ISHIKAWA, S .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 44 (01) :147-150

[9]

Jing Ai Liu, 2002, Mathematical Communications, V7, P113

[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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