Weak convergence theorems for inverse-strongly skew-monotone operators and generalized mixed equilibrium problems in Banach spaces

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• 作者：Junmin Chen (1)
  Tiegang Fan (1) (2)
  
  1. College of Mathematics and Computer ; Hebei University ; Baoding ; 071002 ; China
  2. College of Mechanical and Electrical Engineering ; Hebei Agricultural University ; Baoding ; 071001 ; China
  
• 关键词：47H05 ; 47H09 ; 47J25 ; generalized nonexpansive type mapping ; generalized mixed equilibrium problem ; maximal monotone operator ; inverse ; strongly skew ; monotone operator
• 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：1,201 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, we consider an iterative algorithm for finding the common element of the set of solutions for the generalized mixed equilibrium problems, the common fixed points set of two generalized nonexpansive type mappings, and the set of solutions of the variational inequality for an inverse-strongly skew-monotone operator in Banach spaces. Under mild conditions, the weak convergence theorem is established by using the sunny generalized nonexpansive retraction in Banach spaces. Our results refine, supplement, and extend the corresponding results in (Saewan et al. in Optim. Lett. 8:501-518, 2014), and other results announced by many other authors.