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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.

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