Convergence theorems for nonexpansive semigroups in CAT(0) spaces

被引：37

作者：

Cho, Yeol Je ^{[2
,3
]}

Ciric, Ljubomir ^{[4
]}

Wang, Sheng-hua ^{[1
,5
]}

机构：

[1] Gyeongsang Natl Univ, Dept Math, Jinju 660701, South Korea

[2] Gyeongsang Natl Univ, Dept Math Educ, Jinju 660701, South Korea

[3] Gyeongsang Natl Univ, RINS, Jinju 660701, South Korea

[4] Fac Mech Engn, Belgrade 11000, Serbia

[5] N China Elect Power Univ, Dept Math & Phys, Baoding 071003, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2011年 / 74卷 / 17期

关键词：

Fixed point; CAT(0) space; Nonexpansive mapping; Nonexpansive semigroup; FIXED-POINTS; MAPPINGS;

D O I：

10.1016/j.na.2011.05.082

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let C be a convex and compact subset of a CAT(0) space X. In this paper, we consider the following iterative scheme for a one-parameter nonexpansive semigroup {T (t) : t >= 0} on C: {x1 is an element of C, xn+1 = lambda T (t(n))xn circle plus (1 - lambda)x(n), where lambda is an element of ( 0, 1) and {t(n)} subset of [0, infinity), and we prove that, under certain conditions, {x(n)} converges to a common fixed point of the semigroup {T (t) : t >= 0}. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：6050 / 6059

页数：10

共 24 条

[1]

[Anonymous], 1999, METRIC SPACES NONPOS

[2]

[Anonymous], 2009, INT J MATH ANAL

[3] NONEXPANSIVE NONLINEAR OPERATORS IN A BANACH SPACE [J].

BROWDER, FE .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1965, 54 (04) :1041-&

[4]

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

[5] Common fixed point theorems for a family of non-self mappings in convex metric spaces [J].

Ciric, Ljubomir .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (5-6) :1662-1669

[6] COMMON FIXED POINTS FOR COMMUTING CONTRACTION MAPPINGS [J].

DEMARR, R .

PACIFIC JOURNAL OF MATHEMATICS, 1963, 13 (04) :1139-&

[7]

Dhompongsa S, 2007, J NONLINEAR CONVEX A, V8, P35

[8] Fixed points of uniformly lipschitzian mappings [J].

Dhompongsa, S. ;

Kirk, W. A. ;

Sims, Brailey .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2006, 65 (04) :762-772

[9] Lim's theorems for multivalued mappings in CAT(0) spaces [J].

Dhompongsa, S ;

Kaewkhao, A ;

Panyanak, B .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 312 (02) :478-487

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

Dhompongsa, S. ;

Panyanak, B. .

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

← 1 2 3 →