Let H be a real Hilbert space and S = {T(s) : $0;{leq};s;<;{infty}$} be a nonexpansive semigroup on H such that $F(S);{ eq};{emptyset}$ For a contraction f with coefficient 0 < $alpha$ < 1, a strongly positive bounded linear operator A with coefficient $ar{gamma}$ > 0. Let 0 < $gamma$ < $frac{ar{gamma}}{alpha}$. It is proved that the sequences {$x_t$} and {$x_n$} generated by the iterative method $$x_t;=;t{gamma}f(x_t);+;(I;-;tA){frac{1}{{lambda}_t}};{int_0}^{{lambda}_t};T(s){x_t}ds,$$ and $$x_{n+1};=;{alpha}_n{gamma}f(x_n);+;(I;-;{alpha}_nA)frac{1}{t_n};{int_0}^{t_n};T(s){x_n}ds,$$ where {t}, {${alpha}_n$} $subset$ (0, 1) and {${lambda}_t$}, {$t_n$} are positive real divergent sequences, converges strongly to a common fixed point $ ilde{x};{in};F(S)$ which solves the variational inequality $langle({gamma}f;-;A) ilde{x},;x;-; ilde{x}{ angle};{leq};0$ for $x;{in};F(S)$.