Continuous Selections and Invertibility of Nonsmooth Maps Between Banach Spaces

Milen Ivanov (), Jesús A. Jaramillo (), Sebastián Lajara () and Nadia Zlateva ()
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Milen Ivanov: Radiant Life Technologies Ltd.
Jesús A. Jaramillo: Universidad Complutense de Madrid
Sebastián Lajara: Universidad Complutense de Madrid
Nadia Zlateva: Faculty of Mathematics and Informatics, Sofia University

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 2, No 20, 20 pages

Abstract: 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.

Keywords: Nonsmooth analysis; Inverse mapping theorem; Continuous selection; Pseudo-Jacobian; 49J52; 49J53 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02692-7

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