HUMMEL-SEEBECK METHOD FOR GENERALIZED EQUATIONS UNDER CONDITIONED SECOND FRECHET DERIVATIVE

Abstract

We are concerned with the problem of approximating a locally unique solution of a generalized equation using a Hummel-Seebeck method in a Banach space setting. We provide a local convergence analysis under some very relaxed conditions on the second Fechet derivative introduced by us [1], [5], [18] (for nonlinear equations). Our results compare favorably with the related obtained in [12], [6], which uses the usual Lipschitz and center Lipschitz conditions.