Banach空间中伪压缩映象不动点的迭代逼近.pdf

Banach空间中伪压缩映象不动点的迭代逼近.pdf

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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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