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Banach空间中伪压缩映象不动点的迭代逼近
Journal of Mathematical Research Exposition
Feb., 2008, Vol. 28, No. 1, pp. 169–176
DOI:10.3770/j.issn:1000-341X.2008.01.022
Http://
Approximating Fixed Points of Pseudocontractive
Mapping in Banach Spaces
YAO Yong-hong, CHEN Ru-dong
(Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China)
(E-mail: yuyanrong@)
Abstract Let K be a nonempty closed convex subset of a real p-uniformly convex Banach
space E and T be a Lipschitz pseudocontractive self-mapping of K with F (T ) := {x ∈ K : Tx =
x} = ∅. Let a sequence {x } be generated from x ∈ K by x = a x + b Ty + c u ,
n 1 n+1 n n n n n n
′
′ ′
y = a x + b Tx + c v for all integers n ≥ 1. Then x − Tx → 0 as n → ∞. Moreover,
n n n n n n n n n
if T is completely continuous, then {x } converges strongly to a fixed point of T .
n
Keywords pseudocontractive mappings; p-uniformly convex Banach spaces; Ishikawa iteration
process with errors.
Document code A
MR(2000) Subject Classification 47H05; 47H10; 47H17
Chinese Library Classification O177.91
1. Introduction
Let K be a nonempty subset of a real Banach space E with dual E∗ . We denote by J the
normalized duality mapping from E to 2E ∗ defined by
∗ ∗ ∗ 2 ∗ 2
J (x) = {f ∈ E : x, f = x = f },
where , denotes the generalized d
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