Convergence theorems for λ-strict pseudo-contractions in q-uniformly smooth Banach spaces

被引：16

作者：

Zhou, Hai Yun ^{[1
,2
]}

机构：

[1] Hebei Normal Univ, Coll Math & Informat Sci, Shijiazhuang 050016, Peoples R China

[2] Shijiazhuang Mech Engn Coll, Dept Math, Shijiazhuang 050003, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2010年 / 26卷 / 04期

基金：

中国国家自然科学基金;

关键词：

convergence theorem; lambda-strict pseudo-contraction; the normal Mann iteration; the Ishikawa-like iteration; q-uniformly smooth Banach spaces; NONEXPANSIVE-MAPPINGS; FIXED-POINTS; LIPSCHITZ PSEUDOCONTRACTIONS; ACCRETIVE-OPERATORS; NONLINEAR MAPPINGS; WEAK CONVERGENCE; HILBERT-SPACES; APPROXIMATION; SEMIGROUPS;

D O I：

10.1007/s10114-010-7341-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we continue to discuss the properties of iterates generated by a strict pseudocontraction or a finite family of strict pseudo-contractions in a real q-uniformly smooth Banach space. The results presented in this paper are interesting extensions and improvements upon those known ones of Marino and Xu [Marino, G., Xu, H. K.: Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces. J. Math. Anal. Appl., 324, 336-349 (2007)]. In order to get a strong convergence theorem, we modify the normal Mann's iterative algorithm by using a suitable convex combination of a fixed vector and a sequence in C. This result extends a recent result of Kim and Xu [Kim, T. H., Xu, H. K.: Strong convergence of modified Mann iterations. Nonl. Anal., 61, 51-60 (2005)] both from nonexpansive mappings to lambda-strict pseudo-contractions and from Hilbert spaces to q-uniformly smooth Banach spaces.

引用

页码：743 / 758

页数：16

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