We introduce a class of piecewise-smooth+ mappings and prove the implicit-function theorem for this class. The proof is based on the theorem on global homeomorphism, which follows from the well-known Chernavskii theorem.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 5, pp. 619–625, May, 2008.
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Miklyukov, V.M. Piecewise-smooth+ version of the implicit-function theorem. Ukr Math J 60, 708–715 (2008). https://doi.org/10.1007/s11253-008-0092-x
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DOI: https://doi.org/10.1007/s11253-008-0092-x