Iterative approximation of countable family of relatively nonexpansive mappings and system of equilibrium problems in Banach spaces

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• 作者：Yekini Shehu
• 关键词：Relatively nonexpansive mappings ; Generalized projection operator ; Equilibrium problem ; Banach spaces ; 47H06 ; 47H09 ; 47J05 ; 47J25
• 刊名：Afrika Matematika
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：26
• 期：5-6
• 页码：1049-1069
• 全文大小：570 KB
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• 作者单位：Yekini Shehu (1)
  
  1. Department of Mathematics, University of Nigeria, Nsukka, Nigeria
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics Education
  Applications of Mathematics
  History of Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：2190-7668

文摘

Our purpose in this paper is to construct a new iterative scheme and prove strong convergence theorem using the iterative scheme for approximation of a common fixed point of a countable family of relatively nonexpansive mappings, which is also a solution to a finite system of equilibrium problems in a uniformly convex and uniformly smooth real Banach space. We apply our results to approximate fixed point of a nonexpansive mapping, which is also solution to a finite system of equilibrium problems in a real Hilbert space, and approximate a common solution to finite system of variational inequality problems and convex minimization problems which is also a common solution to countable family of relatively nonexpansive mappings in a uniformly convex and uniformly smooth real Banach space. Our results extend many known recent results in the literature. Keywords Relatively nonexpansive mappings Generalized projection operator Equilibrium problem Banach spaces