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<p>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.</p>

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Continuous Selections and Invertibility of Nonsmooth Maps Between Banach Spaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月29日

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  • Milen Ivanov,
  • Jesús A. Jaramillo,
  • Sebastián Lajara,
  • Nadia Zlateva

摘要

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.