VISCOSITY APPROXIMATION METHODS FOR THE SPLIT EQUALITY COMMON FIXED POINT PROBLEM OF QUASI-NONEXPANSIVE OPERATORS

doi:10.1016/S0252-9602(16)30083-2

数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (5): 1474-1486.doi: 10.1016/S0252-9602(16)30083-2

VISCOSITY APPROXIMATION METHODS FOR THE SPLIT EQUALITY COMMON FIXED POINT PROBLEM OF QUASI-NONEXPANSIVE OPERATORS

赵静¹, 王盛楠²

1. College of Science, Civil Aviation University of China, Tianjin 300300, China Tianjin Key Laboratory for Advanced Signal Processing, Tianjin 300300, China;
2. College of Science, Civil Aviation University of China, Tianjin 300300, China

收稿日期:2014-10-20 修回日期:2015-10-09 出版日期:2016-10-25 发布日期:2016-10-25
通讯作者: Jing ZHAO,zhaojing200103@163.com E-mail:zhaojing200103@163.com
作者简介:Shengnan WANG,shengnan19900507@163.com
基金资助:
The research was supported by National Natural Science Foundation of China (61503385) and Fundamental Research Funds for the Central Universities of China (3122016L002).

VISCOSITY APPROXIMATION METHODS FOR THE SPLIT EQUALITY COMMON FIXED POINT PROBLEM OF QUASI-NONEXPANSIVE OPERATORS

Jing ZHAO¹, Shengnan WANG²

1. College of Science, Civil Aviation University of China, Tianjin 300300, China Tianjin Key Laboratory for Advanced Signal Processing, Tianjin 300300, China;
2. College of Science, Civil Aviation University of China, Tianjin 300300, China

Received:2014-10-20 Revised:2015-10-09 Online:2016-10-25 Published:2016-10-25
Contact: Jing ZHAO,zhaojing200103@163.com E-mail:zhaojing200103@163.com
Supported by:
The research was supported by National Natural Science Foundation of China (61503385) and Fundamental Research Funds for the Central Universities of China (3122016L002).

摘要/Abstract

摘要：

Let H₁, H₂, H₃ be real Hilbert spaces, let A:H₁→H₃, B:H₂→H₃ be two bounded linear operators. The split equality common fixed point problem (SECFP) in the infinite-dimensional Hilbert spaces introduced by Moudafi (Alternating CQ-algorithm for convex feasibility and split fixed-point problems. Journal of Nonlinear and Convex Analysis) is to find x∈F(U), y∈F(T) such that Ax=By, (1) where U:H₁→H₁ and T:H₂→H₂ are two nonlinear operators with nonempty fixed point sets F(U)={x∈H₁:Ux=x} and F(T)={x∈H₂:Tx=x}. Note that, by taking B=I and H₂=H₃ in (1), we recover the split fixed point problem originally introduced in Censor and Segal. Recently, Moudafi introduced alternating CQ-algorithms and simultaneous iterative algorithms with weak convergence for the SECFP (1) of firmly quasi-nonexpansive operators. In this paper, we introduce two viscosity iterative algorithms for the SECFP (1) governed by the general class of quasi-nonexpansive operators. We prove the strong convergence of algorithms. Our results improve and extend previously discussed related problems and algorithms.

关键词: split equality common fixed point problems, quasi-nonexpansive operator, strong convergence, viscosity iterative algorithms, Hilbert space

Abstract:

Key words: split equality common fixed point problems, quasi-nonexpansive operator, strong convergence, viscosity iterative algorithms, Hilbert space

中图分类号:

47H09

赵静, 王盛楠. VISCOSITY APPROXIMATION METHODS FOR THE SPLIT EQUALITY COMMON FIXED POINT PROBLEM OF QUASI-NONEXPANSIVE OPERATORS[J]. 数学物理学报(英文版), 2016, 36(5): 1474-1486.

Jing ZHAO, Shengnan WANG. VISCOSITY APPROXIMATION METHODS FOR THE SPLIT EQUALITY COMMON FIXED POINT PROBLEM OF QUASI-NONEXPANSIVE OPERATORS[J]. Acta mathematica scientia,Series B, 2016, 36(5): 1474-1486.

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VISCOSITY APPROXIMATION METHODS FOR THE SPLIT EQUALITY COMMON FIXED POINT PROBLEM OF QUASI-NONEXPANSIVE OPERATORS

VISCOSITY APPROXIMATION METHODS FOR THE SPLIT EQUALITY COMMON FIXED POINT PROBLEM OF QUASI-NONEXPANSIVE OPERATORS

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