The Equivalence of Mann and Implicit Mann Iterations for Uniformly Pseudocontractive Mappings in Uniformly Smooth Banach Spaces

被引：0
|
作者：
Wang, Cheng [1 ]
Wang, Zhiming [1 ]
机构：
[1] Tangshan Coll, Dept Basic Sci, Tangshan 063000, Peoples R China
来源：
INTELLIGENT STRUCTURE AND VIBRATION CONTROL, PTS 1 AND 2 | 2011年 / 50-51卷
关键词：
Mann iteration; implicit Mann iteration; uniformly pseudocontractive map; generalized Lipschitzian map; uniformly smooth Banach space; LIPSCHITZIAN; CONVERGENCE;
D O I：
10.4028/www.scientific.net/AMM.50-51.718
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
In this paper, suppose E is an arbitrary uniformly smooth real Banach space, and D is a nonempty closed convex subset of E. Let T be a generalized Lipschitzian and uniformly pseudocontractive self-map with F(T) not equal 0. Suppose that {u(n)}(n=1)(infinity), {x(n)}(n=1)(infinity) are defined by Mann iteration and implicit Mann iteration respectively, with the iterative parameter {a(n)}(n=1)(infinity) satisfying certain conditions. Then the above two iterations that converge strongly to fixed point of T are equivalent.
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页码：718 / 722
页数：5
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