Let be an operator from a closed ball of a Banach space to a Banach space . We give new conditions to ensure the convergence of Newton- Kantorovich approximations toward a solution of the equation , under the hypothesis that be Hölder continuous. The case of being Hölder continuous in a generalized sense is analyzed as well.
Cite this article
Espedito De Pascale, P. P. Zabrejko, Convergence of the Newt on- Kantorovich Method under Vertgeim Conditions: a New Improvement. Z. Anal. Anwend. 17 (1998), no. 2, pp. 271–280