期刊
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
卷 73, 期 3, 页码 689-694出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2010.03.058
关键词
Nonexpansive mappings; Iterative method; Variational inequality; Fixed point; Projection; Viscosity approximation
资金
- Tianjin Natural Science Foundation in China [06YFJMJC12500]
- Fundamental Research Funds for the Central Universities [ZXH2009D021]
Let H be a real Hilbert space. Suppose that T is a nonexpansive mapping on H with a fixed point, f is a contraction on H with coefficient 0 < alpha < 1, and F : H -> H is a k-Lipschitzian and eta-strongly monotone operator with k > 0, eta > 0. Let 0 < mu < 2 eta/k(2), 0 < gamma < mu(eta-mu k(2)/2)/alpha = tau/alpha. We proved that the sequence {x(n)} generated by the iterative method x(n+1) = alpha(n)gamma f(x(n)) + (I -mu alpha(n)F)Tx(n) converges strongly to a fixed point (x) over tilde is an element of F(ix) (T), which solves the variational inequality <(gamma f - mu F)(x) over tilde, x-(x) over tilde > <= 0, for x is an element of F(ix)(T). (C) 2010 Elsevier Ltd. All rights reserved.
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