Set-Valued and Variational Analysis

, Volume 27, Issue 4, pp 921–947 | Cite as

Inversion of Nonsmooth Maps between Banach Spaces

  • Jesús A. JaramilloEmail author
  • Sebastián Lajara
  • Óscar Madiedo


We study the invertibility nonsmooth maps between infinite-dimensional Banach spaces. To this end, we introduce an analogue of the notion of pseudo-Jacobian matrix of Jeyakumar and Luc in this infinite-dimensional setting. Using this, we obtain several inversion results. In particular, we give a version of the classical Hadamard integral condition for global invertibility in this context.


Global invertibility Nonsmooth analysis Pseudo-Jacobian Hadamard integral condition 

Mathematics Subject Classification (2010)

49J52 49J53 46G05 


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We would like to thank an anonymous referee for pointing out a mistake in a previous version of this paper, and also for suggesting to consider the regularity of Nemytskii operators.


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© Springer Nature B.V. 2018

Authors and Affiliations

  • Jesús A. Jaramillo
    • 1
    Email author
  • Sebastián Lajara
    • 2
  • Óscar Madiedo
    • 3
  1. 1.Instituto de Matemática Interdisciplinar (IMI) and Departamento de Análisis MatemáticoUniversidad Complutense de MadridMadridSpain
  2. 2.Departamento de MatemáticasUniversidad de Castilla-La Mancha, Escuela de Ingenieros IndustrialesAlbaceteSpain
  3. 3.Departamento de Matemática Aplicada, Ciencia e Ingeniería de los Materiales y Tecnología ElectrónicaUniversidad Rey Juan CarlosMóstolesSpain

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