JournalszaaVol. 17, No. 2pp. 271–280

Convergence of the Newt on- Kantorovich Method under Vertgeim Conditions: a New Improvement

  • Espedito De Pascale

    Università della Calabria, Arcavacata di Rende, Italy
  • P. P. Zabrejko

    The Academy of Sciences of Belarus, Minsk, Belarus
Convergence of the Newt on- Kantorovich Method under Vertgeim Conditions: a New Improvement cover
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Abstract

Let f:B(x0,R)XYf: B(x_0, R) \subset X \to Y be an operator from a closed ball of a Banach space XX to a Banach space YY. We give new conditions to ensure the convergence of Newton- Kantorovich approximations toward a solution of the equation f(x)=0f(x) = 0, under the hypothesis that ff' be Hölder continuous. The case of ff’ 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

DOI 10.4171/ZAA/821