A two-sided error estimate for a regularizing method based on M.M. Lavrent'ev's method

We consider an operator equation of the first kind with error in the operator and in the right-hand side of the equation. The method is a function of this operator depending on a positive parameter $\alpha$. A lower estimate of a method of solving this equation for any value of $\alpha$ is obtained. A regularizing method based on Lavrent'ev's method is constructed, and a two-sided error estimate is obtained for this method. Discrete approximations of Lavrent'ev's method are constructed. Error estimates are obtained for these approximations. The discrete approximations were further used for a perturbation of the operator in the equation.