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

Ioannis K. Argyros

• 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.