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Positivity

, Volume 10, Issue 4, pp 693–700 | Cite as

A Semilocal Convergence of a Secant–Type Method for Solving Generalized Equations

  • Said Hilout
  • Alain Piétrus
Article

Abstract

In this paper we present a study of the existence and the convergence of a secant–type method for solving abstract generalized equations in Banach spaces. With different assumptions for divided differences, we obtain a procedure that have superlinear convergence. This study follows the recent results of semilocal convergence related to the resolution of nonlinear equations (see [11])

Mathematics Subject Classification (2000)

47H04 65K10 

Keywords

Set–valued mapping generalized equation super–linear convergence Aubin continuity divided difference 

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Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  1. 1.Département de Mathématiques Appliquées et Informatique, Faculté des Sciences et Techniques Béni–MellalMaroc
  2. 2.Laboratoire Analyse Optimisation Contrôle, Département de Mathématiques et InformatiqueUniversité des Antilles et de la Guyane Pointe–à–PitreFrance

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