Abstract

Let E be a real Banach space which admits a weakly sequentially continuous duality mapping from E to E*, and K be a nonempty closed convex subset of E. Let {T(t):t\geq 0} be a Lipschitzian pseudocontractive semigroup on K such that $F:=\underset{t\geq 0}{\cap}\Fix(T(t))\ne \emptyset,$ and $f:K\to K$ be a fixed contractive mapping. When {αn}, {tn} satisfy some appropriate conditions, the iterative process given by xn=αnf(xn)+(1-αn)T(tn)xn for n \in N, converges strongly to p\in F, which is the unique solution in F to the following variational inequality: <(f-I)p,j(x-p)> ≤ 0 \forall x\in F. Our results presented in this paper extend and improve recent results of R. Chen and H. He [1], Y. Song and R. Chen [8], Xu [13].