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


  • Ioannis K. Argyros Cameron University.




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.

Author Biography

Ioannis K. Argyros, Cameron University.

Department of Mathematics.


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How to Cite

I. K. Argyros, “A new convergence theorem for the method of tangent hyperbolas in banach space”, Proyecciones (Antofagasta, On line), vol. 18, no. 1, pp. 1-11, Apr. 2018.




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