A general composite iterative method for generalized mixed equilibrium problems, variational inequality problems and optimization problems

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• 作者：Jong Soo Jung (1)
  
• 关键词：generalized mixed equilibrium problem ; fixed point ; nonexpansive mapping ; inverse ; strongly monotone mapping ; variational inequality ; optimization problem ; metric projection ; strongly positive bounded linear operator
• 刊名：Journal of Inequalities and Applications
• 出版年：2011
• 出版时间：December 2011
• 年：2011
• 卷：2011
• 期：1
• 全文大小：317KB
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• 作者单位：Jong Soo Jung (1)
  
  1. Department of Mathematics, Dong-A University, Busan, 604-714, Korea
  
• ISSN：1029-242X

文摘

In this article, we introduce a new general composite iterative scheme for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality problem for an inverse-strongly monotone mapping in Hilbert spaces. It is shown that the sequence generated by the proposed iterative scheme converges strongly to a common element of the above three sets under suitable control conditions, which solves a certain optimization problem. The results of this article substantially improve, develop, and complement the previous well-known results in this area. 2010 Mathematics Subject Classifications: 49J30; 49J40; 47H09; 47H10; 47J20; 47J25; 47J05; 49M05.