Solving variational inclusions by a method obtained using a multipoint iteration formula

• Autores: Catherine Cabuzel, Alain Piétrus
• Localización: Revista matemática complutense, ISSN-e 1988-2807, ISSN 1139-1138, Vol. 22, Nº 1, 2009, págs. 63-74
• Idioma: inglés
• DOI: 10.5209/rev_rema.2009.v22.n1.16314
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• Resumen

  • This paper deals with variational inclusions of the form: 0 e f(x)+F(x) where f is a single function admitting a second order Fréchet derivative and F is a set-valued map acting in Banach spaces. We prove the existence of a sequence (xk) satisfying 0 e f(xk)+?M i=1 aiAf(xk+ßi(xk+1-xk))(xk+1-xk)+F(xk+1) where the single-valued function involved in this relation is an approximation of the function f based on a multipoint iteration formula and we show that this method is locally cubically convergent.