A variant of the Newton-Kantorovich theorem for nonlinear integral equations of mixed Hammerstein type

  1. Ezquerro, J.A. 1
  2. González, D. 1
  3. Hernández, M.A. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Applied Mathematics and Computation

ISSN: 0096-3003

Año de publicación: 2012

Volumen: 218

Número: 18

Páginas: 9536-9546

Tipo: Artículo

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DOI: 10.1016/J.AMC.2012.03.049 SCOPUS: 2-s2.0-84860428902 WoS: WOS:000302992700047 GOOGLE SCHOLAR

Otras publicaciones en: Applied Mathematics and Computation

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Resumen

We study nonlinear integral equations of mixed Hammerstein type using Newton's method as follows. We investigate the theoretical significance of Newton's method to draw conclusions about the existence and uniqueness of solutions of these equations. After that, we approximate the solutions of a particular nonlinear integral equation by Newton's method. For this, we use the majorant principle, which is based on the concept of majorizing sequence given by Kantorovich, and milder convergence conditions than those of Kantorovich. Actually, we prove a semilocal convergence theorem which is applicable to situations where Kantorovich's theorem is not. © 2012 Elsevier Inc. All rights reserved.