Uniformity of the Local Convergence of Chord Method for Generalized Equations

Abstract

Let X be a real or complex Banach space and Y be a normed linear space. Suppose that f:X → Y is a Frechet differentiable function and F:X ⇉ 2 is a set-valued mapping with closed graph. Uniform convergence of Chord method for solving generalized equation y ∈ f x + F x ...... . (∗), where y ∈ Y a parameter, is studied in the present paper. More clearly, we obtain the uniform convergence of the sequence generated by Chord method in the sense that it is stable under small variation of perturbation parameter y provided that the set-valued mapping F is pseudo-Lipschitz at a given point (possibly at a given solution).