A Convergence Theorem for Solving Generalized Mixed Equilibrium Problems and Finding Fixed Points of a Weak Bregman Relatively Nonexpansive Mappings in Banach Spaces

被引:0
作者
Vahid Darvish
Kittisak Jantakarn
Anchalee Kaewcharoen
Nader Biranvand
机构
[1] Nanjing University of Information Science and Technology,School of Mathematics and Statistics
[2] Naresuan University,Department of Mathematics, Faculty of Science
[3] Imam Ali University,Faculty of Sciences
来源
Acta Mathematica Vietnamica | 2022年 / 47卷
关键词
Banach space; Bregman projection; Bregman distance; Weak Bregman relatively nonexpansive mapping; Fixed point; Generalized mixed equilibrium problem; 47H09; 26B25; 47J25; 58C30;
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中图分类号
学科分类号
摘要
In this paper, we study a new iterative method for finding fixed points of a weak Bregman relatively nonexpansive mapping and solutions of generalized mixed equilibrium problems in Banach spaces.
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页码:553 / 569
页数:16
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共 49 条
  • [11] Combettes PL(2006)Bregman distances, totally convex functions and a method for solving operator equations in Banach spaces Abstr. Appl. Anal. Art. ID 84919 1-353
  • [12] Borwein JM(1981)An iterative row-action method for interval convex programming J. Optim. Theory Appl. 34 321-603
  • [13] Reich S(2016)Strong convergence theorem for a system of generalized mixed equilibrium problems and Bregman nonexpansive mapping in Banach spaces Opsearch. 53 584-1344
  • [14] Sabach S(2011)Iterative methods for solving systems of variational inequalities in reflexive Banach spaces SIAM J. Optim. 21 1319-523
  • [15] Bregman LM(2005)Proximal point algorithms with Bregman functions in Banach spaces J. Nonlinear Convex Anal. 6 505-1063
  • [16] Bruck RE(2013)Iterative methods for approximating fixed points of Bregman nonexpansive operators Discrete Contin. Dyn. Syst. Ser. S. 6 1043-348
  • [17] Reich S(2019)Re-examination of Bregman functions and new properties of their divergences Optimization 68 279-371
  • [18] Burnariu D(2018)Solutions to inexact resolvent inclusion problems with applications to nonlinear analysis and optimization Rend. Circ. Mat. Palermo 67 337-485
  • [19] Reich S(2009)A strong convergence theorem for a proximal-type algorithm in reflexive Banach spaces J. Nonlinear Convex Anal. 10 471-116
  • [20] Zaslavski AJ(2011)A projection method for solving nonlinear problems in reflexive Banach spaces J. Fixed Point Theory Appl. 9 101-240