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Variational Analysis
- Publisher
- Springer Journals
- Copyright
- Copyright © 2011 by Springer Science+Business Media B.V.
- Subject
- Mathematics; Mathematics, general; Mechanics; Statistical Physics, Dynamical Systems and Complexity; Computer Science, general; Theoretical, Mathematical and Computational Physics
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- DOI
- 10.1007/s10440-011-9642-6
- Publisher site
- See Article on Publisher Site
Abstract
The aim of this study is the approximation of a solution x ∗ of the generalized equation 0∈f(x)+F(x) in Banach spaces, where f is a single function whose second order Fréchet derivative ∇2 f verifies an Hölder condition, and F stands for a set-valued map with closed graph. Using a fixed point theorem and proceeding by induction under the pseudo-Lipschitz property of F, we obtain a sequence defined by a midpoint formula whose convergence to x ∗ is superquadratic. Taking a weaker condition, we present the result obtained when ∇2 f satisfies a center-Hölder conditioning.
Journal
Acta Applicandae Mathematicae – Springer Journals
Published: Sep 29, 2011