CQ method for generalized mixed equilibrium problem and fixed point problem of infinite family of quasi-?-asymptotically nonexpansive mappings in Banach spaces

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• 作者：Min Liu (1)
  
• 关键词：quasi ; ? ; asymptotically nonexpansive mapping ; generalized mixed equilibrium problem ; the CQ method ; 47H05
• 刊名：Acta Mathematicae Applicatae Sinica, English Series
• 出版年：2014
• 出版时间：October 2014
• 年：2014
• 卷：30
• 期：4
• 页码：931-942
• 全文大小：248 KB
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  12. Takahashi, W., Zembayashi, K. Strong convergence theorems by a new hybrid method for equilibrium problems and relatively nonexpansive mappings. / Fixed Point Theory and Applications, volume 2008, Article ID 528476, 11 pages
  13. Takahashi, W. Nonlinear Functional Analysis. Yokohama Publishers, Yokohama, 2000
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• 作者单位：Min Liu (1)
  
  1. Department of Mathematics, Yibin University, Yibin, 644000, China
  
• ISSN：1618-3932

文摘

In this paper, we prove a strong convergence theorem for finding a common element of the set of solutions for a generalized mixed equilibrium problems, the set of fixed points of infinite family of quasi-?-asymptotically non-expansive mappings in a Banach space by using the CQ method. Our results improve the main results of Takahashi and Takahashi and Takahashi and Zembayashi. Moreover, the method of proof adopted in the paper is different from that of them.