Zeitschrift für Analysis und ihre Anwendungen
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Published online: 1998-06-30
Convergence of the Newt on- Kantorovich Method under Vertgeim Conditions: a New ImprovementEspedito De Pascale and P. P. Zabrejko (1) Università della Calabria, Arcavacata di Rende, Italy
(2) The Academy of Sciences of Belarus, Minsk, Belarus
Let $f: B(x_0, R) \subset X \to Y$ be an operator from a closed ball of a Banach space $X$ to a Banach space $Y$. We give new conditions to ensure the convergence of Newton- Kantorovich approximations toward a solution of the equation $f(x) = 0$, under the hypothesis that $f'$ be Hölder continuous. The case of $f’$ being Hölder continuous in a generalized sense is analyzed as well.
Keywords: Newton-Kantorovich approximations, Hölder type conditions
De Pascale Espedito, Zabrejko P. P.: Convergence of the Newt on- Kantorovich Method under Vertgeim Conditions: a New Improvement. Z. Anal. Anwend. 17 (1998), 271-280. doi: 10.4171/ZAA/821