ABSTRACT
In this chapter we provide convergence results for variational inequalities under Lipschitz{type conditions on the derivatives and Lipschitz{like assumption on set{valued maps.
We present a new approach of the convergence of Chebyshev{type iterative method in Banach space for solving variational inclusions under dierent assumptions used in (cf. [389, 391, 153]). We relax Lipschitz, Holder or center{Holder type conditions by introducing !{type{conditioned second order Frechet derivative. Under this condition, we show that the sequence is locally superquadratically convergent if some Aubin continuity property is satised. In particular, we recover a quadratic and a cubic convergence.
