科研之友
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摘要
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).
- 出版日期2010-8-1
- 单位中国民航大学
