Iterative Scheme for Non-Expansive Semigroups in Hilbert Space

The main result of this paper is that I consider two iterative methods that generate the sequence {x_n}, {y_n} by the algorithm,respectively. x_n=(I-alpha_n)T(t_n)x_n+alpha_ngammaf(x_n), (1.3) y_n+1=(I-alpha_n)T(t_n)y_n+alpha_ngammaf(y_n), (1.4) where {x_n} and {t_n} are two sequences satisfying certain conditions and Omega ={S(t):tges0} is a non-expansive semigroup on H. It is proved that the sequence {x_n}, {y_n} generated by the iterative method (1.3) and (1.4), respectively,converges strongly to a common fixed point x*isin F which solves the variational inequality lang(A-gammaf)x*, x*-zrang les0, Z isin F(Omega).