弱压缩映像下黏性逼近非扩张半群的不动点问题

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.

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

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 {αn},{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).