数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (4): 1081-1097.doi: 10.1016/S0252-9602(14)60071-0

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CONVERGENCE ANALYSIS FOR SYSTEM OF EQUILIBRIUM PROBLEMS AND LEFT BREGMAN STRONGLY RELATIVELY NONEXPANSIVE MAPPING

Yekini SHEHU   

  1. Department of Mathematics, University of Nigeria, Nsukka, Nigeria
  • 收稿日期:2013-05-27 出版日期:2014-07-20 发布日期:2014-07-20

CONVERGENCE ANALYSIS FOR SYSTEM OF EQUILIBRIUM PROBLEMS AND LEFT BREGMAN STRONGLY RELATIVELY NONEXPANSIVE MAPPING

Yekini SHEHU   

  1. Department of Mathematics, University of Nigeria, Nsukka, Nigeria
  • Received:2013-05-27 Online:2014-07-20 Published:2014-07-20

摘要:

In this paper, we prove strong convergence theorems for approximation of a fixed point of a left Bregman strongly relatively nonexpansive mapping which is also a solution to a finite system of equilibrium problems in the framework of reflexive real Banach spaces. We also discuss the approximation of a common fixed point of a family of left Bregman strongly nonexpansive mappings which is also solution to a finite system of equilibrium problems in reflexive real Banach spaces. Our results complement many known recent results in the literature.

关键词: left Bregman strongly relatively nonexpansive mapping, left Bregman projec-tion, equilibrium problem, Banach spaces

Abstract:

In this paper, we prove strong convergence theorems for approximation of a fixed point of a left Bregman strongly relatively nonexpansive mapping which is also a solution to a finite system of equilibrium problems in the framework of reflexive real Banach spaces. We also discuss the approximation of a common fixed point of a family of left Bregman strongly nonexpansive mappings which is also solution to a finite system of equilibrium problems in reflexive real Banach spaces. Our results complement many known recent results in the literature.

Key words: left Bregman strongly relatively nonexpansive mapping, left Bregman projec-tion, equilibrium problem, Banach spaces

中图分类号: 

  • 47H06