Iterative methods with fuzzy feedback for solving irregular operator equations (Q1048554)

Let \(F:H_1\to H_2\) be a (nonlinear) operator between Hilbert spaces. In this article it is assumed that \(F\) is differentiable but it is not assumed that the operator \({F'}^*(x)F'(x)\) is continuously invertible, such that classical iterative schemes (e.g. Newton's method) cannot be used. In the book [\textit{A.\,B. Bakushinsky} and \textit{M.\,Yu. Kokurin}, Iterative methods for approximate solution of inverse problems. Mathematics and its Applications 577. Dordrecht: Springer (2004; Zbl 1070.65038)] the authors proposed and investigated some regularization schemes on the base of the classical Newton-Kantorovich method. In this work the author continues this study, proposing a new generalized iterative process whose convergence is guaranteed in wider conditions (one of the conditions imposed is called ``fuzzy feedback'').