Fixed point property and approximation of a class of nonexpansive mappings

被引：2
|
作者：
Song, Yisheng [1 ,2 ]
Huang, Ying [1 ]
机构：
[1] Henan Normal Univ, Sch Math & Informat Sci, Xinxiang 453007, Henan, Peoples R China
[2] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China
来源：
FIXED POINT THEORY AND APPLICATIONS | 2014年
关键词：
psi-firmly nonexpansive mappings; fixed points; reflexive Banach spaces; Picard iteration; NONLINEAR CONTRACTIONS; CONVERGENCE THEOREMS; WEAK-CONVERGENCE; COMPACTNESS; OPERATORS; SPACES;
D O I：
10.1186/1687-1812-2014-81
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We introduce the concept of psi-firmly nonexpansive mapping, which includes a firmly nonexpansive mapping as a special case in a uniformly convex Banach space. It is shown that every bounded closed convex subset of a reflexive Banach space has the fixed point property for psi-firmly nonexpansive mappings, an important subclass of nonexpansive mappings. Furthermore, Picard iteration of this class of mappings weakly converges to a fixed point.
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页数：11
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