弱压缩映像下黏性逼近非扩张半群的不动点问题

Viscosity Approximation of Common Fixed Points of Nonexpansive Semigroups with Weakly Contractive Mappings

设E是自反的Banach空间且具弱连续正规对偶映像J:E→E*,C E是非空闭凸集.{T(t):t∈R+}:C→C的非扩张半群,且F(T(t))≠φ,f:C→C的弱压缩映像,在{αn},{tn}满足一定的条件下,若{xn}是由(1.3)和(1.4)式分别定义的迭代序列,则xn→q∈F(T(t)),(n→∞),且q是变分不等式的惟一解:〈(f-I)q,j(x-q)≤0,x∈F.

Let E be a real reflexive Banach space which admits a weakly sequentially continuous duality mapping from E to E^＊ ,and C be a nonempty closed convex subset of E.Let {T（ t）：t∈R^＋ }： C→C be a nonexpansive group such that F （ T （ t ） ） ≠ and f： C→C be a weakly contractive mapping, when { an}, {tn} satisfy some appropriate conditions, the two iterative processes were defined （1.3） and （1.4）, thenxn→p ∈ F（ T（t） ）, （n→∞）,which is the unique solution in F to the following variational inequality： （ （f - I） q ,j（ x - q ） ） ≤0, x ∈ F（ T） .