The modified Ishikawa iterative algorithm with errors for a countable family of Bregman totally quasi-D-asymptotically nonexpansive mappings in reflexive Banach spaces

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• 作者：Ren-Xing Ni (1)
  Jen-Chih Yao (2) (3)
  
  1. Department of Mathematics ; Shaoxing University ; Zhejiang ; 312000 ; China
  2. Center for General Education ; China Medical University ; Taichung ; 40402 ; Taiwan
  3. Department of Mathematics ; King Abdulaziz University ; P.O. Box 80203 ; Jeddah ; 21589 ; Saudi Arabia
  
• 关键词：26B25 ; 46T99 ; 47H04 ; 47H05 ; 47H09 ; 47H10 ; 47J05 ; 47J20 ; 47J25 ; 52A41 ; 54C20 ; asymptotically Bregman totally quasi ; D ; asymptotically nonexpansive mapping ; generalized mixed equilibrium problem ; Bregman distance ; Bregman projection ; fixed point ; shrinking projection method ; Banach space
• 刊名：Fixed Point Theory and Applications
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,320 KB
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• 刊物主题：Analysis; Mathematics, general; Applications of Mathematics; Differential Geometry; Topology; Mathematical and Computational Biology;
• 出版者：Springer International Publishing
• ISSN：1687-1812

文摘

In this paper, a new modified Ishikawa iterative algorithm with errors by a shrinking projection method for generalized mixed equilibrium problems and a countable family of uniformly Bregman totally quasi-D-asymptotically nonexpansive mappings is introduced and investigated in the framework of a real Banach space. Strong convergence of the sequence generated by the proposed algorithm is derived under some suitable assumptions. These results are new and develop some recent results in this field.