Iterative algorithm for a family of split equilibrium problems and fixed point problems in Hilbert spaces with applications

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• 作者：Shenghua Wang ; Xiaoying Gong ; Afrah AN Abdou…
• 关键词：47H10 ; 54H25 ; 65J15 ; 90C30 ; split equilibrium problem ; nonexpansive mapping ; split feasible solution problem ; Hilbert space
• 刊名：Fixed Point Theory and Applications
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：2016
• 期：1
• 全文大小：1,668 KB
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• 作者单位：Shenghua Wang (1)
  Xiaoying Gong (2)
  Afrah AN Abdou (3)
  Yeol Je Cho (4) (5)
  
  1. Department of Mathematics and Physics, North China Electric Power University, Baoding, 071003, China
  2. Department of Mathematics and Sciences, Shijiazhuang University of Economics, Shijiazhuang, 050031, China
  3. Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia
  4. Department of Mathematics Education and RINS, Gyeongsang National University, Jinju, 660701, Korea
  5. Center for General Education, China Medical University, Taichung, 40402, Taiwan
  
• 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, we propose an iterative algorithm and, by using the proposed algorithm, prove some strong convergence theorems for finding a common element of the set of solutions of a finite family of split equilibrium problems and the set of common fixed points of a countable family of nonexpansive mappings in Hilbert spaces. An example is given to illustrate the main result of this paper. As an application, we construct an algorithm to solve an optimization problem. Keywords split equilibrium problem nonexpansive mapping split feasible solution problem Hilbert space