On the role of the coefficients in the strong convergence of a general type Mann iterative scheme

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• 作者：Giuseppe Marino (1) (2)
  Luigi Muglia (1)
  
  1. Dipartimento di Matematica ; Universit谩 della Calabria ; Arcavacata di Rende ; CS ; 87036 ; Italy
  2. Department of Mathematics ; King Abdulaziz University ; P.O. Box 80203 ; Jeddah ; 21589 ; Saudi Arabia
  
• 关键词：47H09 ; 58E35 ; 47H10 ; 65J25 ; iterative methods ; nonexpansive mappings ; strongly monotone operators ; dependence on the coefficients ; variational inequality
• 刊名：Journal of Inequalities and Applications
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,299 KB
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• 刊物主题：Analysis; Applications of Mathematics; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1029-242X

文摘

Let H be a Hilbert space. Let \((W_{n})_{n\in\mathbb{N}}\) be a suitable family of mappings. Let S be a nonexpansive mapping and D be a strongly monotone operator. We study the convergence of the general scheme \(x_{n+1}=W_{n}(\alpha_{n}Sx_{n}+(1-\alpha_{n})(I-\mu_{n}D)x_{n}) \) in dependence on the coefficients \((\alpha_{n})_{n\in\mathbb{N}}\) , \((\mu_{n})_{n\in\mathbb{N}}\) .