IJPAM: Volume 40, No. 1 (2007)

SUPERLINEAR CONVERGENCE OF A FAMILY OF
TWO-STEP STEFFENSEN-TYPE METHODS
FOR GENERALIZED EQUATIONS

Saïd Hilout
Department of Applied Mathematics and Computation
Faculty of Sciences and Technics
BP 523, Béni-Mellal, 23000, MOROCCO
e-mail: said_hilout@yahoo.fr


Abstract.We approximate solution of generalized equations in a Banach spaces. We provide sufficient conditions for the local convergence of a family of two-step Steffensen-type algorithms using a fixed points theorem of multiapplications, the usual Hölder continuous condition and the Aubin continuous concept. This study follows the recent result of two-step Steffensen's method related to the resolution of nonlinear equations (see [#!amat!#]).

Received: July 10, 2007

AMS Subject Classification: 47H04, 65K10

Key Words and Phrases: Steffensen's method, set-valued map, generalized equation, Aubin continuity, divided difference

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 40
Issue: 1