Solving Variational Inclusions by a Method Obtained Using a Multipoint Iteration Formula

Abstract

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 (x_k) satisfying 0 ε f(x_k)+∑^M_i=1 a_iΛf(x_k+β_i(x_k+1-x_k))(x_k+1-x_k)+F(x_k+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.