Multipoint method for generalized equations under mild differentiability conditions

Abstract

We are concerned with the problem of approximating a locally unique solution of a generalized equation using a multipoint method in a Banach spaces. In [9]-[11] the authors showed that the previous method is superquadratically (or cubically) convergent when the second Fréchet derivative satisfies the usual Hölder continuity condition (or center--Hölder continuity condition). Here, we weaken these conditions by using $\omega$--condition (or $\sigma$--condition) on the second derivative introduced by us [1]-[4],[22] (for nonlinear equations), with $\omega$ and $\sigma $ a non--decreasing continuous real functions. We provide also an improvement of the ratio of our algorithm under some $\omega$--center--condition (or $\sigma$--center--condition) and less computational cost.