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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.27 n.3 Antofagasta dic. 2008

http://dx.doi.org/10.4067/S0716-09172008000300007 

 

Proyecciones Journal of Mathematics
Vol. 27, Nº 3, pp. 319-330, December 2008.
Universidad Católica del Norte
Antofagasta - Chile


ON THE LOCAL CONVERGENCE OF A TWO-STEP STEFFENSEN-TYPE METHOD FOR SOLVING GENERALIZED EQUATIONS


IOANNIS K. ARGYROS 1
SAÏD HILOUT 2

1 Cameron university, U. S. A.
2 University Morocco, Morocco.


Correspondencia a:



Abstract
We use a two-step Steffensen-type method [1], [2], [4], [6], [13]-[16] to solve a generalized equation in a Banach space setting under Hölder-type conditions introduced by us in [2], [6] for nonlinear equations. Using some ideas given in [4], [6] for nonlinear equations, we provide a local convergence analysis with the following advantages over related [13]-[16]: finer error bounds on the distances involved, and a larger radius of convergence. An application is also provided.


Key words : Banach space, Steffensen´s method, generalized equation, Aubin continuity, Hölder continuity, radius of convergence, divided difference, set- valued map.


AMS Subject Classification : 65K10, 65G99, 47H04, 49M15.

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

SAÏD HILOUT
Faculty of Science & Technics of Béni-Mellal
Department of Applied Mathematics & Computation
B. P. 523, Béni-Mellal 23000,
Morocco
e-mail : said_hilout@yahoo.fr

Received : October 2008. Accepted : November 2008

 

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