Solving Variational Inclusions by a Method Obtained Using a Multipoint Iteration Formula - Cabuzel, Catherine; Pietrus, Alain (Revista Matemática Complutense, 2009)
This paper deals with variational inclusions of the form: 0 ε 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 ε f(xk)+∑M i=1 aiΛf(xk+βi(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.