Bartle-Graves Theorem Revisited

  • Asen L. DontchevEmail author


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.


Implicit function theorem Metric regularity Continuous selection Variational inequality Differential inclusion 

Mathematics Subject Classification (2010)

47J06 49J53 34A60 49J40 54C65 


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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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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Aerospace EngineeringThe University of MichiganAnn ArborUSA

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