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Iterative methods for solving nonlinear irregular operator equations in banach space

We present an approach to constructing stable methods for solving nonlinear operator equations in Banach space without anyassumptions on the regularity of the operator. The approach is based on the linearization of the equation and the use of aregularization algorithm to find an approximate solution of the linearized equation at each iteration. The local convergence of proposed methods is proved and the estimations of the rate of convergence are established, provided that solution satisfies a sourcewise representation condition. The case of noisy data is also analysed.