Continuous Selections and Invertibility of Nonsmooth Maps Between Banach Spaces
Abstract In the setting of Banach spaces, we address the problems of local surjectivity, existence of a continuous selection and invertibility for nonsmooth maps which admit a suitable pseudo-Jacobian. We obtain a general sufficient condition for the existence of a continuous selection. As a consequence, we recover from our result the classical Bartle-Graves selection theorem for linear maps. We also obtain a sufficient condition for local invertibility, which in particular applies to certain Gâteaux differentiable maps.
Authors
- Sebastián Lajara (ORCID: https://orcid.org/0000-0002-8422-9536)
- Nadia Zlateva (ORCID: https://orcid.org/0000-0002-6223-9055)
- Jesús Á. Jaramillo (ORCID: https://orcid.org/0000-0002-0197-6449)
- Milen Ivanov (ORCID: https://orcid.org/0000-0002-2387-0450)
Institutions
- Universidad Complutense de Madrid (ES)
- Institute of Mathematical Sciences (ES)
- Sofia University "St. Kliment Ohridski" (BG)
Publication Details
- Journal
- Journal of Optimization Theory and Applications
- Published
- 2025-05-29
- DOI
- https://doi.org/10.1007/s10957-025-02692-7
- Primary Topic
- Advanced Differential Equations and Dynamical Systems
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- European Commission
- Universidad Complutense de Madrid
- Bulgarian National Science Fund
- Ministerio de Ciencia e Innovación
- European Regional Development Fund
- Agencia Estatal de Investigación