Ray's theorem revisited: a fixed point free firmly nonexpansive mapping in Hilbert spaces

被引：0

作者：

Kohsaka, Fumiaki ^{[1
]}

机构：

[1] Oita Univ, Dept Comp Sci & Intelligent Syst, Oita, Oita 8701192, Japan

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2015年

基金：

日本学术振兴会;

关键词：

firmly nonexpansive mapping; fixed point; Hilbert space; Ray's theorem; unbounded set; BANACH-SPACES; UNBOUNDED SETS; PROPERTY;

D O I：

10.1186/s13660-015-0606-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give another proof of a strong version of Ray's theorem ensuring that every unbounded closed convex subset of a Hilbert space admits a fixed point free firmly nonexpansive mapping.

引用

页码：1 / 3

页数：3

共 12 条

[1]

[Anonymous], 2000, Nonlinear Functional Analysis

[2]

Aoyama K, 2010, J NONLINEAR CONVEX A, V11, P335

[3]

Brezis H., 2011, Functional analysis, DOI DOI 10.1007/978-0-387-70914-7

[4] FIXED-POINT THEOREMS FOR NONCOMPACT MAPPINGS IN HILBERT SPACE [J].

BROWDER, FE .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1965, 53 (06) :1272-&

[5] CONVERGENCE THEOREMS FOR SEQUENCES OF NONLINEAR OPERATORS IN BANACH SPACES [J].

BROWDER, FE .

MATHEMATISCHE ZEITSCHRIFT, 1967, 100 (03) :201-&

[6] NONEXPANSIVE PROJECTIONS ON SUBSETS OF BANACH SPACES [J].

BRUCK, RE .

PACIFIC JOURNAL OF MATHEMATICS, 1973, 47 (02) :341-355

[7]

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

[8]

Goebel K., 1990, Topics in Metric Fixed Point Theory

[9]

Kohsaka F, 2011, ADV INTEL SOFT COMPU, V100, P403

[10] THE FIXED-POINT PROPERTY AND UNBOUNDED SETS IN HILBERT-SPACE [J].

RAY, WO .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1980, 258 (02) :531-537

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