Hybrid algorithm for common solution of monotone inclusion problem and fixed point problem and applications to variational inequalities

被引：4
|
作者：
Zhang, Jingling [1 ]
Jiang, Nan [1 ]
机构：
[1] Tianjin Univ, Dept Math, Tianjin 300350, Peoples R China
来源：
SPRINGERPLUS | 2016年 / 5卷
基金：
中国国家自然科学基金;
关键词：
Quasi-nonexpansive mappings; Inverse-strongly monotone mapping; Maximal monotone operator; Fixed point; CONVERGENCE THEOREMS; EQUILIBRIUM PROBLEMS; NONEXPANSIVE-MAPPINGS; ITERATIVE ALGORITHM; ACCRETIVE OPERATOR; ZERO-POINT; APPROXIMATION; ELEMENTS;
D O I：
10.1186/s40064-016-2389-9
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
The aim of this paper is to investigate hybrid algorithm for a common zero point of the sum of two monotone operators which is also a fixed point of a family of countable quasi-nonexpansive mappings. We point out two incorrect proof in paper (Hecai in Fixed Point Theory Appl 2013:11, 2013). Further, we modify and generalize the results of Hecai's paper, in which only a quasi-nonexpansive mapping was considered. In addition, two family of countable quasi-nonexpansive mappings with uniform closeness examples are provided to demonstrate our results. Finally, the results are applied to variational inequalities.
引用
收藏
页数：13
相关论文
共 50 条
  • [31] STRONG CONVERGENCE THEOREM FOR SPLIT COMMON FIXED POINT PROBLEM AND HIERARCHICAL VARIATIONAL INEQUALITY PROBLEM IN HILBERT SPACES
    Takahashi, Wataru
    Wen, Ching-Feng
    Yao, Jen-Chih
    JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2020, 21 (01) : 251 - 273
  • [32] ITERATIVE ALGORITHM OF SPLIT MONOTONE VARIATIONAL INCLUSION PROBLEM FOR NEW MAPPINGS
    Farid, Mohammad
    Irfan, Syed Shakaib
    Ahmad, Iqbal
    KRAGUJEVAC JOURNAL OF MATHEMATICS, 2024, 48 (04): : 493 - 513
  • [33] Iterative common solutions for monotone inclusion problems, fixed point problems and equilibrium problems
    Takahashi, Wataru
    Wong, Ngai-Ching
    Yao, Jen-Chih
    FIXED POINT THEORY AND APPLICATIONS, 2012,
  • [34] Iterative algorithm of common solutions for a constrained convex minimization problem, a quasi-variational inclusion problem and the fixed point problem of a strictly pseudo-contractive mapping
    Yifen Ke
    Changfeng Ma
    Fixed Point Theory and Applications, 2014
  • [35] Iterative algorithm of common solutions for a constrained convex minimization problem, a quasi-variational inclusion problem and the fixed point problem of a strictly pseudo-contractive mapping
    Ke, Yifen
    Ma, Changfeng
    FIXED POINT THEORY AND APPLICATIONS, 2014,
  • [36] Strong convergence theorems for the split equality variational inclusion problem and fixed point problem in Hilbert spaces
    Guo, Haili
    He, Huimin
    Chen, Rudong
    FIXED POINT THEORY AND APPLICATIONS, 2015, : 1 - 18
  • [37] Monotone inclusion problem and fixed point problem of a generalized demimetric mapping in CAT(0) spaces
    Ugwunnadi, G. C.
    Collins, O. C.
    Magagula, V. M.
    Khan, A. R.
    RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 2021, 70 (01) : 365 - 387
  • [38] A regularization algorithm for a common solution of generalized equilibrium problem, fixed point problem and the zero points of the sum of two operators
    Ming Tian
    Si-Wen Jiao
    Journal of Inequalities and Applications, 2015
  • [39] HYBRID METHOD FOR DESIGNING EXPLICIT HIERARCHICAL FIXED POINT APPROACH TO MONOTONE VARIATIONAL INEQUALITIES
    Ceng, Lu-Chuan
    Lin, Yen-Cherng
    Petrusel, Adrian
    TAIWANESE JOURNAL OF MATHEMATICS, 2012, 16 (04): : 1531 - 1555
  • [40] Strong Convergence of a System of Generalized Mixed Equilibrium Problem, Split Variational Inclusion Problem and Fixed Point Problem in Banach Spaces
    Abbas, Mujahid
    Ibrahim, Yusuf
    Khan, Abdul Rahim
    de la Sen, Manuel
    SYMMETRY-BASEL, 2019, 11 (05):
12345