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The convergence ball of Newton’s method and the uniqueness ball of equations under Hölder-type continuous derivatives. (English) Zbl 1052.65054
For Newton’s method applied to a nonlinear operator equation with a Fréchet differentiable operator in a Banach space, the optimal radius of the convergence ball is investigated. The optimality of the radius is proved for equations with a continuous derivative operator of Hölder-type. Also, another optimal estimate of the radius of the uniqueness ball of the equation, in the same type of hypothesis, is obtained.

65J15 Numerical solutions to equations with nonlinear operators (do not use 65Hxx)
47J25 Iterative procedures involving nonlinear operators
Full Text: DOI
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