STRONG CONVERGENCE THEOREMS FOR SEMIGROUPS OF NOT NECESSARILY CONTINUOUS MAPPINGS IN BANACH SPACES

被引：0

作者：

Takahashi, Wataru ^{[1
,2
,3
]}

机构：

[1] China Med Univ, China Med Univ Hosp, Res Ctr Interneural Comp, Taichung 40447, Taiwan

[2] Keio Univ, Keio Res & Educ Ctr Nat Sci, Kouhoku Ku, Yokohama, Kanagawa 2238521, Japan

[3] Tokyo Inst Technol, Dept Math & Comp Sci, Meguro Ku, Tokyo 1528552, Japan

来源：

JOURNAL OF NONLINEAR AND CONVEX ANALYSIS | 2019年 / 20卷 / 04期

关键词：

Attractive point; Banach space; fixed point; generalized nonspreading mapping; invariant mean; strong converegence; nonexpansive semigroup; strongly asymptotically invariant net; FIXED-POINT THEOREMS; GENERALIZED HYBRID MAPPINGS; MAXIMAL MONOTONE-OPERATORS; NONLINEAR ERGODIC-THEOREMS; PROXIMAL-TYPE ALGORITHM; NONEXPANSIVE-MAPPINGS; ATTRACTIVE POINT; NONSPREADING MAPPINGS; WEAK; APPROXIMATION;

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, using a class of semigroups of not necessarily continuous mappings in a Banach space which includes discrete semigroups of generalized nonspreading mappings and semigroups of phi-nonexpansive mappings, we establish a strong convergence theorem of Halpern's type iteration for the semigroups of mappings in a Banach space. Using the result, we obtain well-known and new theorems which are connected with strong convergence results in Hilbert spaces and Banach spaces. It seems that such a strong convergence theorem is first for classes of semigroups of not necessarily continuous mappings in a Banach space.

引用

页码：603 / 623

页数：21

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