A variational inequality in complete CAT(0) spaces

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• 作者：Hadi Khatibzadeh ; Sajad Ranjbar
• 关键词：47H10 ; 47J20 ; 47J25 ; Hadamard space ; fixed point ; variational inequality ; nonexpansive mapping ; $${\Delta}$$ 螖 ; convergence ; strong convergence
• 刊名：Journal of Fixed Point Theory and Applications
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：17
• 期：3
• 页码：557-574
• 全文大小：662 KB
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• 作者单位：Hadi Khatibzadeh (1)
  Sajad Ranjbar (1)
  
  1. Department of Mathematics, University of Zanjan, P.O. Box 45195-313, Zanjan, Iran
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Analysis
  Mathematical Methods in Physics
  
• 出版者：Birkh盲user Basel
• ISSN：1661-7746

文摘

In this paper, first, existence of solutions for a variational inequality associated with a nonexpansive mapping in Hadamard spaces is studied. Then, the inexact proximal point algorithm for approximation of a solution of the variational inequality, which is also a fixed point of the nonexpansive mapping, is proposed. We prove the \({\Delta}\)-convergence of the generated sequence by the algorithm as well as the strong convergence of a Halpern-type regularization one to a fixed point of the nonexpansive mapping. Our motivation is to give a step toward investigation of variational inequalities in CAT(0) spaces. Keywords Hadamard space fixed point variational inequality nonexpansive mapping \({\Delta}\)-convergence strong convergence