where a nonlinear operator acts on a pair of Hilbert spaces () is considered in the paper. The element is approximately known, . The operator is Fréchet differentiable and satisfies the conditions and for any . The original problem is ill-posed, particularly the solution of (1) with the exact data may be nonunique. The following iteratively regularized scheme is used to minimize a functional . Here is an element of and a source type condition is fulfilled; is a function of a spectral parameter and . A novel generalized discrepancy principle
where is suggested in the paper. It is proved (under a source type condition) that if is chosen by (2), then , where is a solution of (1). Convergence rates for various generating functions are obtained.