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.
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页码：743 / 758
页数：16
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