Iterative Lavrentiev regularization method under a heuristic rule for nonlinear ill-posed operator equations

In this paper, we consider the iterative Lavrentiev regularization method for obtaining a stable approximate solution nonlinear ill-posed operator equation $F(x)=y$, where $ F:D(F) \subset X \rightarrow X$ is monotone on Hilbert spaces $X$. order to obtain using methods, it important use suitable stopping rule terminate iterations at appropriate step. Recently, Qinian Jin and Wei Wang (2018) have proposed heuristic stop iteratively regularized Gauss-Newton method. The advantage of over existing priori posteriori rules that does not require accurate information noise level, which may be available or reliable in practical applications. propose an iterated method.We derive error estimates under nonlinearity conditions $F$.