Abstract
We consider the classical inverse mapping theorem of Nash and Moser from the angle of some recent development by Ekeland and the authors. Geometrisation of tame estimates coupled with certain ideas coming from variational analysis when applied to a directionally differentiable mapping produces very general surjectivity result and, if injectivity can be ensured, inverse mapping theorem with the expected Lipschitz-like continuity of the inverse. We also present a brief application to differential equations.
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Acknowledgements
Sincere thanks are due to anonymous referees for their valuable suggestions and comments. Research is supported by the Bulgarian National Scientific Fund under Grant KP-06-H22/4.
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Communicated by Michel Théra.
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Ivanov, M., Zlateva, N. Inverse mapping theorem in Fréchet spaces. J Optim Theory Appl 190, 300–315 (2021). https://doi.org/10.1007/s10957-021-01885-0
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DOI: https://doi.org/10.1007/s10957-021-01885-0