FIXED POINT AND NONLINEAR ERGODIC THEOREMS FOR NEW NONLINEAR MAPPINGS IN HILBERT SPACES

被引：0

作者：

Kawasaki, Toshiharu ^{[1
]}

Takahashi, Wataru ^{[2
]}

机构：

[1] Nihon Univ, Coll Engn, Fukushima 9638642, Japan

[2] Tokyo Inst Technol, Dept Math & Comp Sci, Tokyo 1528552, Japan

来源：

JOURNAL OF NONLINEAR AND CONVEX ANALYSIS | 2012年 / 13卷 / 03期

基金：

日本学术振兴会;

关键词：

Fixed point theorem; ergodic theorem; Hilbert space; contraction mapping; nonexpansive mapping; nonspreading mapping; hybrid mapping; generalied hybrid mapping; WEAK-CONVERGENCE THEOREMS; NONEXPANSIVE-MAPPINGS; OPERATORS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we introduce a broad class of nonlinear mappings which covers the class of contractive mappings and the class of generalized hybrid mappings in a Hilbert space. Then we prove a fixed point theorem for such mappings in a Hilbert space. Furthermore, we prove a nonlinear ergodic theorem of Baillon's type in a Hilbert space. These results generalize the fixed point theorem and the nonlinear ergodic theorem proved by Kocourek, Takahashi and Yao [9].

引用

页码：529 / 540

页数：12

共 17 条

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[8] COMMON FIXED-POINT THEORY OF SINGLEVALUED MAPPINGS AND MULTIVALUED MAPPINGS
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[9] FIXED POINT THEOREMS AND WEAK CONVERGENCE THEOREMS FOR GENERALIZED HYBRID MAPPINGS IN HILBERT SPACES
Kocourek, Pavel
Takahashi, Wataru
Yao, Jen-Chih
[J]. TAIWANESE JOURNAL OF MATHEMATICS, 2010, 14 (06): : 2497 - 2511
[10] EXISTENCE AND APPROXIMATION OF FIXED POINTS OF FIRMLY NONEXPANSIVE-TYPE MAPPINGS IN BANACH SPACES
Kohsaka, Fumiaki
Takahashi, Wataru
[J]. SIAM JOURNAL ON OPTIMIZATION, 2008, 19 (02) : 824 - 835

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