Viscosity Approximation of Common Fixed Points of Nonexpansive Semigroups with Weakly Contractive Mappings
WU Xianbin · Journal of Chengdu University · 2008
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).