Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (1): 70-79.

• Articles • Previous Articles     Next Articles

Convergence Analysis for Countable Family of Weak Bregman Relatively Nonexpansive Mappings

 CHEN Jia-Wei1, WAN Zhong-Peng2, ZHAO Lie-Ji3   

  1. 1.School of Mathematics and Statistics, Southwest University, Chongqing 400715;
    2.School of Mathematics and Statistics, Wuhan University, Wuhan 430072;
    3.Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, Korea
  • Received:2012-04-19 Revised:2013-08-17 Online:2014-02-25 Published:2014-02-25
  • Supported by:

    国家自然科学基金(71171150)和中央高校基本科研业务专项基金(201120102020004)资助.

Abstract:

A notion of countable family of weak Bregman relatively nonexpansive mappings is introduced in reflexive Banach space. We construct two iterative algorithms for finding a common fixed point of a countable family of weak Bregman relatively nonexpansive mappings in Banach spaces. Finally, the strong convergence of the proposed algorithms are also proved under appropriate conditions.

Key words: Strong convergence theorem, Bregman distance, Bregman projection, (weak) Bregman relatively nonexpansive map

CLC Number: 

  • 47H09
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