MATHEMATICA BOHEMICA, Vol. 133, No. 3, pp. 313-320 (2008)

On a secant-like method for solving
generalized equations

Ioannis K. Argyros, Sa\"{i}d Hilout

Ioannis K. Argyros, Cameron university, Department of Mathematics Sciences, Lawton, OK 73505, USA, e-mail:; {\it Sa\"{i}d Hilout}, Département d'Applications des Mathématiques, Université de Poitiers, bd. Marie & Pierre Curie, Téléport 2, BP 30179, 86962 Futuroscope Chasseneuil Cedex, France, e-mail:

Abstract: In the paper by Hilout and Piétrus (2006) a semilocal convergence analysis was given for the secant-like method to solve generalized equations using Hölder-type conditions introduced by the first author (for nonlinear equations). Here, we show that this convergence analysis can be refined under weaker hypothesis, and less computational cost. Moreover finer error estimates on the distances involved and a larger radius of convergence are obtained.

Keywords: secant-like method, generalized equations, Aubin continuity, radius of convergence, divided difference

Classification (MSC2000): 65G99, 65K10, 49M15

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