A nonlinear ill-posed operator equation , from the domain of the Hilbert space into a Hilbert space , is considered in case of only noisy data are available, with the assumption , . The Tikhonov regularization method consists in using the Tikhonov functional
The convergence rates for this type of regularization under a mild regularity assumption on the solution, namely source conditions of logarithmic type, are proved. For the choice of the regularization parameter a priori or a posteriori strategies according to the discrepancy can be used. Restrictions on the nonlinearity of the forward operator are made unless the initial error is sufficiently smooth.