A posteriori stopping rule for regularized fixed point iterations

Iteratively regularized fixed-point iteration schemexn+1=xn-αn{F(xn)-fδ+εn(xn-x0)}xn+1=xn-αn{F(xn)-fδ+εn(xn-x0)}combined with the generalized discrepancy principle∥F(xN)-fδ∥2⩽τδ<∥F(xn)-fδ∥2,0⩽n1,for solving nonlinear operator equation F(x)=fF(x)=f in a Hilbert space is studied in the paper. It is shown that if FF is monotone and Lipschitz-continuous the sequence {N(δ)}{N(δ)} is admissible, i.e.equation(1)limδ→0∥xN(δ)-x*∥=0,where x*x* is a solution to F(x)=fF(x)=f.