Ioannis K. Argyros

Department of Mathematical Sciences

Cameron University

OK 73505 Lawton, USA

e-mail: iargyros@cameron.edu

Abstract. We provide a finer local convergence analysis than before [6]-[9] of a certain superquadratic method for solving generalized equations under Hölder continuity conditions.

Keywords and phrases. Superquadratic convergence, generalized equations, radius of convergence, Aubin continuity, pseudo-Lipschitz map.

2000 Mathematics Subject Classification. Primary: 65K10, 65G99. Secondary: 47H04, 49M15.

Resumen. Nosotros hacemos un análisis de convergencia local más fino que el proporcionado antes de [6]-[9] de cierto método supercuadrático para resolver ecuaciones generalizadas bajo ciertas condiciones de continuidad de Hölder.

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[1] I. K. Argyros, A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space, J. Math. Anal. Applic. 298 (2004), 374-397.         [ Links ]

[2] I. K. Argyros, Approximate Solution of Operator Equations with Applications, World Scientific Publ. Comp., New Jersey, USA, 2005.         [ Links ]

[3] I. K. Argyros, On the secant method for solving nonsmooth equations, J. Math. Anal. Applic. (to appear, 2006).         [ Links ]

[4] I. K. Argyros, D. Chen, & M. Tabatabai, The Halley-Werner method in Banach spaces, Revue d'Analyse Numerique et de theorie de l'Approximation, 1 (1994), 1-14.         [ Links ]

[5] J. P. Aubin, Lipschitz behavior of solutions to convex minimization problems, Math. Oper. Res. 9 (1984), 87-111.         [ Links ]

[6] J. P. Aubin & H. Frankowska, Set Valued Analysis, Birkhäuser, Boston, 1990.         [ Links ]

[7] A. L. Dontchev, Local convergence of the Newton method for generalized equations, C.R.A.S. Paris 332 Ser. I (1996), 327-331.         [ Links ]

[8] A. L. Dontchev & W. W. Hager, An inverse function theorem for set-valued maps, Proc. Amer. Math. Soc. 121 (1994), 481-489.         [ Links ]

[9] M. H. Geoffroy & A. A. Pietrus, Superquadratic method for solving gener- alized equations in the Hölder case, Ricerche di Matematica LII fasc. 2 (2003), 231-240.         [ Links ]

[10] A. D. Ioffe & V. M. Tikhomirov, Theory of Extremal Problems, North Hol- land, Amsterdam, 1979.         [ Links ]

[11] S. M. Robinson, Strong regular generalized equations, Math. Oper. Res. 5 (1980), 43-62.        [ Links ]

(Recibido en marzo de 2006. Aceptado en mayo de 2006)