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

• 论文 • 上一篇    下一篇

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

赵静1, 王盛楠2   

  1. 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. 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:

Let H1, H2, H3 be real Hilbert spaces, let A:H1H3, B:H2H3 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 xF(U), yF(T) such that Ax=By, (1) where U:H1H1 and T:H2H2 are two nonlinear operators with nonempty fixed point sets F(U)={xH1:Ux=x} and F(T)={xH2: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:

Let H1, H2, H3 be real Hilbert spaces, let A:H1H3, B:H2H3 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 xF(U), yF(T) such that Ax=By, (1) where U:H1H1 and T:H2H2 are two nonlinear operators with nonempty fixed point sets F(U)={xH1:Ux=x} and F(T)={xH2: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.

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

中图分类号: 

  • 47H09