  In this paper, we deal with nonlinear ill-posed problems involving monotone
operators and consider Lavrentiev's regularization method. This approach, in
contrast to Tikhonov's regularization method, does not make use of the adjoint
of the derivative. There are plenty of qualitative and quantitative convergence
results in the literature, both in Hilbert and Banach spaces. Our aim here is
mainly to contribute to convergence rates results in Hilbert spaces based on
some types of error estimates derived under various source conditions and to
interpret them in some settings. In particular, we propose and investigate new
variational source conditions adapted to these Lavrentiev-type techniques.
Another focus of this paper is to exploit the concept of approximate source
conditions.
