数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (5): 1433-1444.doi: 10.1016/S0252-9602(16)30079-0

• 论文 • 上一篇    下一篇

STRONG CONVERGENCE THEOREMS FOR EQUILIBRIUM PROBLEM AND BREGMAN TOTALLY QUASI-ASYMPTOTICALLY NONEXPANSIVE MAPPING IN BANACH SPACES

朱胜, 黄建华   

  1. Institute of Mathematics and Computer Science, Fuzhou University, Fuzhou 350002, China
  • 收稿日期:2015-01-18 修回日期:2015-10-12 出版日期:2016-10-25 发布日期:2016-10-25
  • 通讯作者: Jianhua HUANG,fjhjh57@163.com E-mail:fjhjh57@163.com
  • 作者简介:Sheng ZHU,jxsrsheng@163.com
  • 基金资助:

    This research was supported by the Province Natural Science Foundation of China (2014J01008).

STRONG CONVERGENCE THEOREMS FOR EQUILIBRIUM PROBLEM AND BREGMAN TOTALLY QUASI-ASYMPTOTICALLY NONEXPANSIVE MAPPING IN BANACH SPACES

Sheng ZHU, Jianhua HUANG   

  1. Institute of Mathematics and Computer Science, Fuzhou University, Fuzhou 350002, China
  • Received:2015-01-18 Revised:2015-10-12 Online:2016-10-25 Published:2016-10-25
  • Contact: Jianhua HUANG,fjhjh57@163.com E-mail:fjhjh57@163.com
  • Supported by:

    This research was supported by the Province Natural Science Foundation of China (2014J01008).

摘要:

In this paper, we propose a new hybrid iterative scheme for finding a common solution of an equilibrium problem and fixed point of Bregman totally quasi-asymptotically nonexpansive mapping in reflexive Banach spaces. Moreover, we prove some strong convergence theorems under suitable control conditions. Finally, the application to zero point problem of maximal monotone operators is given by the result.

关键词: equilibrium problem, Bregman totally quasi-asymptotically nonexpansive mapping, Bregman distance, reflexive Banach space

Abstract:

In this paper, we propose a new hybrid iterative scheme for finding a common solution of an equilibrium problem and fixed point of Bregman totally quasi-asymptotically nonexpansive mapping in reflexive Banach spaces. Moreover, we prove some strong convergence theorems under suitable control conditions. Finally, the application to zero point problem of maximal monotone operators is given by the result.

Key words: equilibrium problem, Bregman totally quasi-asymptotically nonexpansive mapping, Bregman distance, reflexive Banach space

中图分类号: 

  • 26A18