Approximation of Common Fixed Points of Nonexpansive Semigroups in Hilbert Spaces
Dan Zhang, Xiaolong Qin, Feng Gu · Journal of Applied Mathematics · 2012
Let H be a real Hilbert space. Consider on H a nonexpansive semigroup S = {T(s) : 0 ≤ s 0. Let /α. It is proved that the sequence {xn} generated by the iterative method 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).