Abstract
We give a new convergence analysis of a two-step method of higher order with a decomposition of a Banach space valued operator. Convergence is studied under generalized center-Lipschitz and restricted Lipschitz conditions for Frechet derivatives of the first and second order and for divided differences of the first order. This approach gives a larger convergence region and more accurate estimations of errors. Numerical experiments are used to complement the theory.
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