A GENERAL VISCOSITY APPROXIMATION METHOD OF FIXED POINT SOLUTIONS OF VARIATIONAL INEQUALITIES FOR NONEXPANSIVE SEMIGROUPS IN HILBERT SPACES

Let H be a real Hilbert space and S = {T(s) : 0 <= s <= infinity} be a nonexpansive semigroup on H such that F(S) not equal empty set. For a contraction f with coefficient 0 < alpha < 1, a strongly positive bounded linear operator A with coefficient (gamma) over bar > 0. Let 0 < gamma < (gamma) over bar/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)1/lambda(t)integral(lambda t)(0) T(s)x(t)ds, and x(n+1) = alpha(n)gamma f(x(n)) + (I - alpha(n)A)1/t(n)integral integral(lambda t)(0) T(s)x(n)ds, where {t}, {alpha(n)} subset of (0,1) and {lambda(t)}, {t(n)} are positive real divergent sequences, converges strongly to a common fixed point (x) over bar epsilon F(S) which solves the variational inequality <(gamma f - A)(x) over bar, x - (x) over bar <= 0 for x epsilon F(S).