Applications of Bregman-Opial Property to Bregman Nonspreading Mappings in Banach Spaces

被引:10
|
作者
Naraghirad, Eskandar [1 ]
Wong, Ngai-Ching [2 ]
Yao, Jen-Chih [3 ]
机构
[1] Univ Yasuj, Dept Math, Yasuj 75918, Iran
[2] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 804, Taiwan
[3] Kaohsiung Med Univ, Ctr Gen Educ, Kaohsiung 807, Taiwan
关键词
FIXED-POINT THEOREMS; STRONG-CONVERGENCE; WEAK-CONVERGENCE;
D O I
10.1155/2014/272867
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The Opial property of Hilbert spaces and some other special Banach spaces is a powerful tool in establishing fixed point theorems for nonexpansive and, more generally, nonspreading mappings. Unfortunately, not every Banach space shares the Opial property. However, every Banach space has a similar Bregman-Opial property for Bregman distances. In this paper, using Bregman distances, we introduce the classes of Bregman nonspreading mappings and investigate the Mann and Ishikawa iterations for these mappings. We establish weak and strong convergence theorems for Bregman nonspreading mappings.
引用
收藏
页数:14
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