A Uniparametric Family of Iterative Processes for Solving Non-Differentiable Equations

  1. Hernández, M.A. 1
  2. Rubio, M.J. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Journal of Mathematical Analysis and Applications

ISSN: 0022-247X

Año de publicación: 2002

Volumen: 275

Número: 2

Páginas: 821-834

Tipo: Artículo

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DOI: 10.1016/S0022-247X(02)00432-8 SCOPUS: 2-s2.0-0037113727 WoS: WOS:000179956200024 GOOGLE SCHOLAR

Otras publicaciones en: Journal of Mathematical Analysis and Applications

Repositorio institucional: lock_openAcceso abierto Editor

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Resumen

In this work we study a class of secant-like iterations for solving nonlinear equations in Banach spaces. We consider a condition for divided differences which generalizes the usual ones, i.e., Lipschitz and Hölder continuous conditions. A semilocal convergence result is obtained for nondifferentiable operators. For that, we use a technique based on a new system of recurrence relations to obtain domains of existence and uniqueness of the solution. Finally, we apply our results to the numerical solution of several examples. © 2002 Elsevier Science (USA). All rights reserved.