A new convergence theorem for the method of tangent hyperbolas in banach space

• Argyros, Ioannis K. ^[1]
  1. [1] Cameron University

     Cameron University

     Estados Unidos

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 18, Nº. 1, 1999, págs. 1-11
• Idioma: inglés
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• Resumen

  • In this study we appmximate a locally unique solution of a non-linear operator equtation in Banach space using the method of tangent hyperbolas. A new semilocal convergence theorem is provided using Lipschitz conditions on the second Fréchet-derivative. Our conditions are different than earlier ones. Hence, they have theorctical and practical value. Numerical examples are also provoded.