Approximation of Common Fixed Points of Nonexpansive Semigroups in Hilbert Spaces

Abstract

Let H be a real Hilbert space. Consider on H a nonexpansive semigroup S={T(s):0≤s 0. Let 0<γ<γ¯/α. It is proved that the sequence {xn} generated by the iterative method x0∈H, xn+1=αnγf(xn)+βnxn+((1-βn)I-αnA)(1/sn)∫0snT(s)xnds, 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).