Approximation of Common Fixed Points of Nonexpansive Semigroups in Hilbert Spaces

[摘要] LetHbe a real Hilbert space. Consider onHa nonexpansive semigroupS={T(s):0≤s<∞}with a common fixed point, a contractionfwith the coefficient0<α<1, and a strongly positive linear bounded self-adjoint operatorAwith the coefficientγ¯>  0. Let0<γ<γ¯/α. It is proved that the sequence{xn}generated by the iterative methodx0∈H, xn+1=αnγf(xn)+βnxn+((1-βn)I-αnA)(1/sn)∫0snT(s)xnds, n≥0converges strongly to a common fixed pointx*∈F(S), whereF(S)denotes the common fixed point of the nonexpansive semigroup. The pointx*solves the variational inequality〈(γf-A)x*,x-x*〉≤0for allx∈F(S).

[学科分类] 应用数学