Convergence of the method of chords for solving generalized equations

In this article, we study an iterative procedure of the following form , where f is a function and F is a set valued map acting from a Banach space X to a linear normed space Y, for solving generalized equations. We show that this method is locally Q-linearly convergent to a solution x* of the generalized equation if the set-valued map is Aubin continuous at (0, x*) with a constant M for growth, f: X → Y is a function, whose Fréchet derivative is L-Lipschitz and A ∈ L(X,Y) is such that 2M∥Δf(x*) − A∥ < 1. We also study the stability of this method. The research of this paper is partially supported by a Technical University of Varna internal research grant number 487/2008.