On the local convergence of a midpoint method in banach spaces under a gamma-type condition

  • Ioannis K. Argyros Cameron University.
Palabras clave: Midpoint method, Banach space, Gamma—type condition, Radius of convergence, Local convergence, Fréchet—derivative.

Resumen

In this study we are concerned with the problem of approximating a locally unique solution of an operator equation in a Banach space setting using the midpoint method, introduced by us in [5], [6]. Here, we use gamma-type condition to provide a local convergence analysis. Our results compare favorably with the relevant ones in [9], [11], [12]-[14]- In particular our radius of convergence is larger. Numerical examples are also provided.

Biografía del autor/a

Ioannis K. Argyros, Cameron University.
Department of Mathematical Sciences.

Citas

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[9] Homeir, H. H. H. A modified Newton method for root finding with cubic convergence, J. Comput. Appl. Math., 157, pp. 227—230, (2003).

[10] Kantorovich, L. V., and Akilov, G. P. Functional Analysis in normed spaces, Pergamon Press, Oxford, (1982).

[11] Ozban, A. Y. Some new variants of Newton’s method, Appl. Math. Letters, 17, pp. 677—682, (2004).

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[14] Zhao, F. and Wang, D. The theory of Smale’s point estimation and its applications, J. Comput. Appl. Math., 60, pp. 253—269, (1995).
Cómo citar
Argyros, I. (1). On the local convergence of a midpoint method in banach spaces under a gamma-type condition. Proyecciones. Journal of Mathematics, 28(2), 155-167. https://doi.org/10.4067/S0716-09172009000200005
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