Iterative Methods for Generalized Split Feasibility Problems in Hilbert Spaces

被引：146

作者：

Takahashi, Wataru ^{[1
,3
,4
]}

Xu, Hong-Kun ^{[1
]}

Yao, Jen-Chin ^{[1
,2
,5
]}

机构：

[1] Kaohsiung Med Univ, Dept Appl Math, Kaohsiung 80424, Taiwan

[2] King Abdulaziz Univ, Dept Math, Jeddah 21589, Saudi Arabia

[3] Keio Univ, Keio Res & Educ Ctr Nat Sci, Yokohama, Kanagawa 2238521, Japan

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

[5] Kaohsiung Med Univ, Ctr Fundamental Sci, Kaohsiung 80702, Taiwan

来源：

SET-VALUED AND VARIATIONAL ANALYSIS | 2015年 / 23卷 / 02期

基金：

日本学术振兴会;

关键词：

Generalized hybrid mapping; Averaged mapping; Maximal monotone operator; Inverse strongly monotone operator; Resolvent; Fixed point; Iteration procedure; Split feasibility problem; WEAK-CONVERGENCE THEOREMS; VISCOSITY APPROXIMATION METHODS; FIXED-POINT THEOREMS; NONEXPANSIVE-MAPPINGS; ALGORITHM;

D O I：

10.1007/s11228-014-0285-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Generalized split feasibility problems governed by generalized hybrid mappings are studied via iterative methods. Several algorithms are introduced to solve them. In particular, weak convergence of these algorithms is proved. As tools, averaged mappings and resolvents of maximal monotone operators are technically maneuvered to facilitate the argument of the proofs to the main results. Applications to Mann's iteration method for nonexpansive mappings and to equilibrium problems are included.

引用

页码：205 / 221

页数：17

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