Construction of majorizing sequences for operators with unbounded second derivative

  1. Ezquerro Fernández, José Antonio
  2. González Sánchez, Daniel
  3. Hernández Verón, Miguel Angel
Book:
Eleventh International Conference Zaragoza-Pau on Applied Mathematics and Statistics

Publisher: Universidad de Zaragoza

ISBN: 9788415538158

Year of publication: 2012

Pages: 123-132

Type: Book chapter

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Abstract

The aim of this paper is to construct majorizing sequences for Newton’smethod in Banach spaces, when the second Fréchet derivative of the operator involved is unbounded, and prove then the semilocal convergence of the method. The new results are illustrated with a nonlinear integral equation of mixed Hammerstein type.