NONEXPANSIVE SET-VALUED MAPPINGS IN METRIC AND BANACH SPACES

被引：0

作者：

Dhompongsa, S. ^{[1
]}

Kirk, W. A. ^{[2
]}

Panyanak, B. ^{[1
]}

机构：

[1] Chiang Mai Univ, Dept Math, Fac Sci, Chiang Mai 50200, Thailand

[2] Univ Iowa, Dept Math, Iowa City, IA 52242 USA

来源：

JOURNAL OF NONLINEAR AND CONVEX ANALYSIS | 2007年 / 8卷 / 01期

关键词：

Nonexpansive mappings; CAT(0) spaces; fixed points; set-valued mappings;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We extend recent homotopy results of Sims, Xu, and Yuan for set-valued maps to a CAT(0) setting. We also introduce art ultrapower approach to proving fixed point theorems for nonexpansive set-valued mappings, both in this setting and in Banach spaces. This method provides an efficient. way of recovering all of the classical Banach space results.

引用

页码：35 / 45

页数：11

共 25 条

[1]

[Anonymous], 1990, NONSTANDARD METHODS

[2]

Bridson M.R., 1999, METRIC SPACES NONPOS

[3]

BROWN KS, 1989, BUILDINGS

[4]

BURAGO D., 2001, A course in metric geometry, V33, DOI 10.1090/gsm/033

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

Dhompongsa, S. ;

Kirk, W. A. ;

Sims, Brailey .

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

[6] 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

[7]

Dominguez Benavides T., 2004, ANN U MARIA CURIE, V58, P37

[8]

DOWNING D, 1977, MATH JAPONICAE, V22, P99

[9] MULTIVALUED NONEXPANSIVE MAPPINGS AND OPIALS CONDITION [J].

DOZO, EL .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 38 (02) :286-292

[10]

Goebel K., 1984, Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings

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