Construction of majorizing sequences for operators with unbounded second derivative

1. Ezquerro Fernández, José Antonio
2. González Sánchez, Daniel
3. Hernández Verón, Miguel Angel

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The aim of this paper is to construct majorizing sequences for Newton’smethod in Banach spaces, when the second Fréchet derivative of the operator involved is unbounded, and prove then the semilocal convergence of the method. The new results are illustrated with a nonlinear integral equation of mixed Hammerstein type.