WEAK AND STRONG CONVERGENCE THEOREMS FOR EXTENDED HYBRID MAPPINGS IN HILBERT SPACES

被引:0
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作者
Takahashi, Wataru [1 ]
Wong, Ngai-Ching [2 ]
Yao, Jen-Chih [3 ]
机构
[1] Tokyo Inst Technol, Dept Math & Comp Sci, Tokyo 1528552, Japan
[2] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 80424, Taiwan
[3] Kaohsiung Med Univ, Ctr Gen Educ, Kaohsiung 80702, Taiwan
关键词
Hilbert space; nonexpansive mapping; nonspreading mapping; hybrid mapping; fixed point; mean convergence; FIXED-POINT THEOREMS; STRICT PSEUDO-CONTRACTIONS; NONEXPANSIVE-MAPPINGS; NONLINEAR MAPPINGS; APPROXIMATION; OPERATORS;
D O I
暂无
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let C be a closed convex subset of a real Hilbert space II. A mapping U : C -> H is called extended hybrid if there are alpha, beta, gamma is an element of R such that alpha(1 + gamma)parallel to Ux -Uy parallel to(2) + (1 - alpha(1 - gamma))parallel to x - Uy parallel to(2) <= (beta + alpha gamma)parallel to Ux - y parallel to(2) + (1 - (beta + alpha gamma))parallel to x - y parallel to(2) -(alpha - beta)gamma parallel to x - Ux parallel to(2) - gamma parallel to y - Uy parallel to(2) for all x,y is an element of C. In this paper, we first show that the class of extended hybrid mappings contains the class of strict pseudo-contractions defined by Browder and Petryshyn [6]. We also obtain some important properties for extended hybrid mappings and strict pseudo-contractions in a Hilbert space. Using these results, we prove weak convergence theorems of Baillon's type [3] and of Mann's type [19] for extended hybrid mappings in a Hilbert space. Finally, we get strong convergence theorems of Halpern's type [9] and of the hybrid methods [22] and [30] for these mappings.
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页码:553 / 575
页数:23
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