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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.27 no.1 Antofagasta May 2008

http://dx.doi.org/10.4067/S0716-09172008000100001 

Proyecciones Journal of Mathematics
Vol. 27, Nº 1, pp. 1-14, May 2008.
Universidad Católica del Norte
Antofagasta - Chile


ON THE LOCAL CONVERGENCE OF A NEWTON—TYPE METHOD IN BANACH SPACES UNDER A GAMMA—TYPE CONDITION


IOANNIS K. ARGYROS 1
SAÏD HILOUT 2

1 Cameron university, U.S.A.
2 Poitiers University, France.

Correspondencia a:



Abstract
We provide a local convergence analysis for a Newton—type method to approximate a locally unique solution of an operator equation in Banach spaces. The local convergence of this method was studied in the elegant work by Werner in [11], using information on the domain of the operator. Here, we use information only at a point and a gamma—type condition [4], [10]. It turns out that our radius of convergence is larger, and more general than the corresponding one in [10]. Moreover the same can hold true when our radius is compared with the ones given in [9] and [11]. A numerical example is also provided.


Key words : Banach space, Newton—type method, local convergence, gamma—type condition, local convergence, Fréchet—derivative, radius
of convergence.
AMS Classification [2000] : 65G99, 65K10, 47H17, 49M15.

REFERENCES
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IOANNIS K. ARGYROS
Department of Mathematics Sciences
Cameron university
Lawton, OK 73505
U. S. A.
e-mail : mailto:ioannisa@cameron.edu

SAÏD HILOUT
Laboratoire de Mathématiques et Applications
Poitiers University
Bd. Pierre et Marie Curie, Téléport 2
B. P. 30179
86962 Futuroscope Chasseneuil Cedex
France
e-mail : mailto:said.hilout@math.univ—poitiers.fr

Received : November 2007. Accepted : January 2008


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