ASYMPTOTIC BEHAVIOR OF NONEXPANSIVE MAPPINGS IN FINITE DIMENSIONAL NORMED SPACES

被引：0

作者：

Lins, Brian ^{[1
]}

机构：

[1] Hampden Sydney Coll, Dept Math & Comp Sci, Hampden Sydney, VA 23943 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2009年 / 137卷 / 07期

关键词：

NON-EXPANSIVE MAPPINGS; BANACH-SPACES; ITERATIONS; MAPS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

If X is a finite dimensional real normed space, C is a closed convex subset of X and f : C -> C is nonexpansive with respect to the norm on X, then we show that either f has a fixed point in C or there is a linear functional phi is an element of X* such that lim(k ->infinity) phi(f(k)(x)) = infinity for all x is an element of C.

引用

页码：2387 / 2392

页数：6

共 19 条

[1]

[Anonymous], 1970, CONVEX ANAL

[2]

[Anonymous], GRADUATE STUDIES MAT

[3]

BEARDON AF, 1990, J LOND MATH SOC, V41, P141

[4]

Calka A., 1984, Colloq. Math., V48, P219

[5]

Dafermos C. M., 1973, Journal of Functional Analysis, V13, P97, DOI 10.1016/0022-1236(73)90069-4

[6]

EDELSTEIN M, 1964, P CAMB PHILOS SOC, V60, P439

[7]

Gunawardena J., 1995, Hewlett-Packard Technical Report

[8]

Karlsson A, 2001, ERGOD THEOR DYN SYST, V21, P1447

[9]

KARLSSON A., 2006, Int. J. Math. Math. Sci., V2006

[10] INVARIANT HALF-LINES OF NONEXPANSIVE PIECEWISE-LINEAR TRANSFORMATIONS [J].

KOHLBERG, E .

MATHEMATICS OF OPERATIONS RESEARCH, 1980, 5 (03) :366-372

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