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

  • Ioannis K. Argyros Cameron University.
Palabras clave: Banach space, Method of tangent hyperbolas, Fréchet - derivative, Newton - Kantorovich hypothesis


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.

Biografía del autor/a

Ioannis K. Argyros, Cameron University.
Department of Mathematics.


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Cómo citar
Argyros, I. (2018). A new convergence theorem for the method of tangent hyperbolas in banach space. Proyecciones. Journal of Mathematics, 18(1), 1-11. https://doi.org/10.22199/S07160917.1999.0001.00001