Almost stability of the Mann type iteration method with error term involving strictly hemicontractive mappings in smooth Banach spaces
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- 作者：Nawab Hussain (1)
Arif Rafiq (2)
Ljubomir B Ciric (3)
Saleh Al-Mezel (1) - 关键词：Mann iteration method with error term ; strictly hemicontractive operators ; strongly pseudocontractive operators ; local strongly pseudocontractive operators ; continuous mappings ; Lipschitz mappings ; smooth Banach spaces
- 刊名：Journal of Inequalities and Applications
- 出版年：2012
- 出版时间：December 2012
- 年：2012
- 卷：2012
- 期：1
- 全文大小：200KB
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Arif Rafiq (2)
Ljubomir B Ciric (3)
Saleh Al-Mezel (1)
1. Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia
2. Hajvery University, 43-52 Industrial Area, Gulberg-III, Lahore, Pakistan
3. Faculty of Mechanical Engineering, University of Belgrade, Al. Rudara 12-35, Belgrade, 11 070, Serbia - ISSN：1029-242X
文摘
Let K be a nonempty closed bounded convex subset of an arbitrary smooth Banach space X and be a continuous strictly hemicontractive mapping. Under some conditions, we obtain that the Mann iteration method with error term converges strongly to a unique fixed point of T and is almost T-stable on K. As an application of our results, we establish strong convergence of a multi-step iteration process.