Fixed point and weak convergence theorems for point-dependent λ-hybrid mappings in Banach spaces

被引：27

作者：

Huang, Young-Ye ^{[2
]}

Jeng, Jyh-Chung ^{[3
]}

Kuo, Tian-Yuan ^{[4
]}

Hong, Chung-Chien ^{[1
]}

机构：

[1] Natl Pingtung Univ Sci & Technol, Dept Ind Management, Neopu 91201, Pingtung, Taiwan

[2] So Taiwan Univ, Ctr Gen Educ, Tainan 71005, Taiwan

[3] Nanjeon Inst Technol, Tainan 73746, Taiwan

[4] Fooyin Univ, Kaohsiung 83102, Taiwan

来源：

FIXED POINT THEORY AND APPLICATIONS | 2011年

关键词：

fixed point; Bregman distance; Gateaux differentiable; subdifferential; NONLINEAR MAPPINGS; ERGODIC-THEOREMS;

D O I：

10.1186/1687-1812-2011-105

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this article is to study the fixed point and weak convergence problem for the new defined class of point-dependent lambda-hybrid mappings relative to a Bregman distance D (f) in a Banach space. We at first extend the Aoyama-Iemoto-Kohsaka-Takahashi fixed point theorem for lambda-hybrid mappings in Hilbert spaces in 2010 to this much wider class of nonlinear mappings in Banach spaces. Secondly, we derive an Opial-like inequality for the Bregman distance and apply it to establish a weak convergence theorem for this new class of nonlinear mappings. Some concrete examples in a Hilbert space showing that our extension is proper are also given. 2010 MSC: 47H09; 47H10.

引用

页码：1 / 15

页数：15

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