Almost stability of the Mann type iteration method with error term involving strictly hemicontractive mappings in smooth Banach spaces

被引：5

作者：

Hussain, Nawab ^{[1
]}

Rafiq, Arif ^{[2
]}

Ciric, Ljubomir B. ^{[3
]}

Al-Mezel, Saleh ^{[1
]}

机构：

[1] King Abdulaziz Univ, Dept Math, Jeddah 21589, Saudi Arabia

[2] Hajvery Univ, Lahore, Pakistan

[3] Univ Belgrade, Fac Mech Engn, Belgrade 11070, Serbia

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2012年

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; PSEUDO-CONTRACTIVE MAPPINGS; FIXED-POINT ITERATION; OPERATORS; EQUATIONS; ISHIKAWA;

D O I：

10.1186/1029-242X-2012-207

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let K be a nonempty closed bounded convex subset of an arbitrary smooth Banach space X and T : K -> K 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.

引用

页数：11

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