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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References
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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCMv43n1a01,
AUTHOR = {Jean-Alexis, Célia and Pietrus, Alain},
TITLE = {{Superquadratic convergence of a Hummel-Seebeck type method}},
JOURNAL = {Revista Colombiana de Matemáticas},
YEAR = {2009},
volume = {43}, ]]>
number = {1},
pages = {1-8}
}