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Chain rules for linear openness in metric spaces and applications

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Abstract

In this work we present a general theorem concerning chain rules for linear openness of set-valued mappings acting between metric spaces. As particular cases, we obtain classical and also some new results in this field of research, including the celebrated Lyusternik–Graves Theorem. The applications deal with the study of the well-posedness of the solution mappings associated to parametric systems. Sharp estimates for the involved regularity moduli are given.

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Acknowledgments

The authors are indebted to the referees for their valuable comments and suggestions. This work was supported by a grant of the Romanian National Authority for Scientific Research, CNCS—UEFISCDI, project number PN-II-ID-PCE-2011-3-0084.

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Authors and Affiliations

  1. Faculty of Mathematics, “Al. I. Cuza” University, Bd. Carol I, nr. 11, 700506 , Iasi, Romania

    Marius Durea

  2. Department of Mathematics, “Gh. Asachi” Technical University, Bd. Carol I, nr. 11, 700506 , Iasi, Romania

    Radu Strugariu

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  1. Marius Durea
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  2. Radu Strugariu
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Correspondence to Radu Strugariu.

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Durea, M., Strugariu, R. Chain rules for linear openness in metric spaces and applications. Math. Program. 143, 147–176 (2014). https://doi.org/10.1007/s10107-012-0598-8

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  • DOI: https://doi.org/10.1007/s10107-012-0598-8

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