Approximation of common fixed points of nonexpansive semigroups in Hilbert spaces

Let h be a real hilbert space. consider on h a nonexpansive semigroup s = {t(s): 0 ≤ s < ∞} with a common fixed point,a contraction f with the coefficient 0 < α < 1,and a strongly positive linear bounded self-adjoint operator a with the coefficient γ̄ > 0. let 0 < γ < γ̄/α. it is proved that the sequence {x n} generated by the iterative method x 0 ∈ h,x n+1 = α nγf(x n) + β nx n + ((1 - β n) i - α n a) (1/s n) ∫ 0 sn t(s)x nds,n ≥ 0 converges strongly to a common fixed point x* ∈ f(s),where f(s) denotes the common fixed point of the nonexpansive semigroup. the point x* solves the variational inequality 〈(γf - a)x*,x - x*〉 ≤ 0 for all x ∈ f(s). copyright © 2012 dan zhang et al.