¹Université des Antilles et de la Guyane, Pointe--à--Pitre, France. Email: celia.jean-alexis@univ-ag.fr
²Université des Antilles et de la Guyane, Pointe--à--Pitre, France. Email: apietrus@univ-ag.fr

The cubic convergence of a method inspired by a Hummel and Seebeck for solving variational inclusions, has been showed when the second order Fréchet derivative of some function f satisfies a Lipschitz condition. Here, we prove the superquadratic convergence of this method whenever this second order Fréchet derivative satisfies a Hölder condition.

Key words: Set-valued mappings, M-pseudo-Lipschitzness, superquadratic convergence, Hölder-type condition.

La convergencia cúbica de un método de Hummel y Seebeck para resolver inclusiones variacionales ha sido probado cuando la derivada de Fréchet de segundo orden de alguna función f satisface una condición de Lipschitz. Aquí probamos la convergencia supercuadrática de este método siempre que esta derivada de Fréchet de segundo orden satisfaga una condición de Hölder.

Palabras clave: Aplicaciones conjunto-valoradas, pseudo-Lipschitz, convergencia supercuadrática, condición de tipo Hölder.

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