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Metric Regularity for Set-Valued Maps in Fréchet-Montel Spaces. Implicit Mapping Theorem

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Abstract

This paper is devoted to new derivative criterion of metric regularity for set-valued map from a Fréchet-Montel space to a Fréchet space. Such type of criteria have been well studied in Banach spaces. Our work extends recent studies motivated by Nash-Moser-Ekeland approach. As a consequence of our criterion, an implicit mapping result is also given in the paper.

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Acknowledgements

Part of the research was done during the visits of N. Zlateva in Brest in 2020 and 2022. She expresses her gratitude to the Laboratoire de Mathématiques de Bretagne Atlantique for hospitality.

The authors express their sincere gratitude for the comments of the anonymous referee.

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Authors and Affiliations

  1. Radiant Life Technologies Ltd, Nicosia, Cyprus

    M. Ivanov

  2. Univ Brest, CNRS UMR 6205 Laboratoire de Mathematiques de Bretagne Atlantique, 6, avenue Victor Le Gorgeu, 29200, Brest, France

    M. Quincampoix

  3. Faculty of Mathematics and Informatics, Sofia University, 5, James Bourchier blvd., 1164, Sofia, Bulgaria

    N. Zlateva

Authors
  1. M. Ivanov
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  2. M. Quincampoix
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  3. N. Zlateva
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Correspondence to M. Quincampoix.

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The work of the first and the third named author is supported by the Bulgarian National Fund for Scientific Research under Contract KP-06-H22/4.

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Ivanov, M., Quincampoix, M. & Zlateva, N. Metric Regularity for Set-Valued Maps in Fréchet-Montel Spaces. Implicit Mapping Theorem. Set-Valued Var. Anal 31, 18 (2023). https://doi.org/10.1007/s11228-023-00679-y

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