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Bartle-Graves Theorem Revisited

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Abstract

We take a fresh look at the Bartle-Graves theorem pointing out the main differences with the standard implicit function theorem. We then present a set-valued version of this theorem which generalizes some recent results. Applications to variational inequalities and differential inclusions are also given.

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Acknowledgments

The author wishes to thank Francisco Aragón Artacho, Evgeny Avakov and the anonymous referees for their helpful comments on previous versions of the manuscript.

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  1. Department of Aerospace Engineering, The University of Michigan, Ann Arbor, MI, USA

    Asen L. Dontchev

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  1. Asen L. Dontchev
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Correspondence to Asen L. Dontchev.

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Supported by the National Science Foundation Award Number CMMI 1562209, the Austrian Science Foundation (FWF) Grant P31400-N32, and the Australian Research Council (ARC) Project DP160100854.

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Dontchev, A.L. Bartle-Graves Theorem Revisited. Set-Valued Var. Anal 28, 109–122 (2020). https://doi.org/10.1007/s11228-019-00524-1

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  • DOI: https://doi.org/10.1007/s11228-019-00524-1

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