On error estimation for the quasi-inversion method for solving a semi-linear ill-posed problem

In this paper, the approximate solutions error estimates are obtained for an ill-posed semi-linear Cauchy problem. The continuity module of the inverse operator is used as a standard estimator for obtaining the error estimates. The value of the continuity module is calculated for two classes of uniform regularization of the original problem. The quasi-inversion method is used to construct stable approximate solutions.