Lavrent'ev regularization of ill-posed problems containing nonlinear near-to-monotone operators with application to autoconvolution equation

In this paper the method of Lavrent'ev for regularization of ill-posed problems with near-to-monotone operators is considered. An a priori rule of choice of the parameter of regularization is presented and the corresponding error estimate is derived. The theory is applied to the autoconvolution equation. Numerical examples are provided.