Semi-local convergence of a derivative-free method for solving equations
Problemy analiza, Tome 10 (2021) no. 2, pp. 18-26.

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We present the semi-local convergence analysis of a two-step derivative-free method for solving Banach space valued equations. The convergence criteria are based only on the first derivative and our idea of recurrent functions.
Keywords: Banach space, derivative-free method, semi-local convergence.
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G. Argyros; M. Argyros; I. K. Argyros; S. George. Semi-local convergence of a derivative-free method for solving equations. Problemy analiza, Tome 10 (2021) no. 2, pp. 18-26. http://geodesic.mathdoc.fr/item/PA_2021_10_2_a1/

[1] Appell J. De., Pascale E., Evkhuta N. A., Zabrejko P. P., “On the two step Newton method for the solution of nonlinear equations”, Math. Nachr., 172 (1995), 5–14 | DOI | MR | Zbl

[2] Argyros I. K., Computational Theory of Iterative Methods, Studies in Computational Mathematics, 15, eds. Chui C.K., Wuytack L., Elsevier Publ. Company, New York, 2007 | Zbl

[3] Argyros I. K., George S., Mathematical modeling for the solution of equations and systems of equations with applications, v. IV, Nova Publishes, NY, 2020 | MR

[4] Ezquerro J. A., Hernandez M. A., “An improvement of the region of accessibility of Chebyshev's method from Newton's method”, Math. Comput., 78 (2009), 1613–1627 | DOI | MR | Zbl

[5] Ezquerro J. A., Hernandez M. A., Magrenan A. A., “Stating points for Newton's method under a center Lipschitz condition for the second derivative”, J. Comput. Appl. Math., 330 (2018), 721–731 | DOI | MR | Zbl

[6] Kantorovich L. V., Akilov G. P., Functional Analysis, Pergamon, Oxford, 1982 | MR | Zbl

[7] Magreñán A. A., Argyros I. K., “Two-step Newton methods”, Journal of Complexity, 30:4 (2014), 533–553 | DOI | MR | Zbl

[8] Potra F. A., Ptak V., Nondiscrete induction and iterative processes, Research notes in Mathematics, 103, Pitman Boston, M.A., 1984 | MR | Zbl