Hilbert空间中非扩张半群的隐格式广义迭代程序

设H为实Hilbert空间,在H上考虑具有公共不动点的非扩张半群f={T(S):sE≥0),具有常数0<α<1的压缩映象f,和具有系数γ>0的强正线性有界算了A.设0<γ<γ/α,文章证明了由下列产生的序列{xn},强收敛于f={T(s):sE≥0}的某一公共不动点x3∈F(T),且x3是下列变分不等式的唯一解.〈(γf-A)x3,z-x3〉F0,对任意的z∈F(T)。

Implicit General Iterative Process for Nonexpansive Semigroups in Hilbert Space

Let H be real Hilbert space. Consider on H a nonexpansive semigroup F={T(s): s≥0} with a common fixedpoint, a contraction f with coefficient 0<α<1, and a strongly positive linear bounded operator A with coefficient γ->0. Let 0<γ<γ-/α. It is proved that the sequence {xn} generated iteratively by (x)converges strongly to a common fixed point x* ∈ F(g)which solves the variational inequality <(γf-A) x*, z-x*>≤0 forz∈F(g)