Ivanov, MilenJaramillo Aguado, Jesús ÁngelLajara, SebastiánZlateva, Nadia2025-05-302025-05-302025Ivanov, M., Jaramillo, J.A., Lajara, S. et al. Continuous Selections and Invertibility of Nonsmooth Maps Between Banach Spaces. J Optim Theory Appl 206, 41 (2025).0022-32391573-287810.1007/s10957-025-02692-7https://hdl.handle.net/20.500.14352/1206562025 Acuerdos Transformativos CRUEIn 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.engAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/journal articlehttps://link.springer.com/article/10.1007/s10957-025-02692-7open accessContinuous selectionInverse mapping theoremNonsmooth analysisPseudo-JacobianAnálisis funcional y teoría de operadores1202 Análisis y Análisis Funcional