Abstract
The concept of majorizing sequences is employed to provide a convergence analysis for Newton-like methods in a Banach space. We use Hölder and center-Hölder continuity assumptions on the Fréchet-derivative of the operators involved. This way we show that our convergence conditions are weaker; error bounds on the distances involved finer and the location of the solution more precise than in earlier results.
Citation
Ioannis K. Argyros. "Concerning the convergence of Newton-like methods under weak Hölder continuity conditions." Funct. Approx. Comment. Math. 31 7 - 22, 2003. https://doi.org/10.7169/facm/1538186639
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