We present a new proof of the theorem which is one of the main results of the p-regularity theory. This gives us a detailed description of the structure of the zero set of a singular nonlinear mapping. We say that F : X → Y is singular at some point x 0 , where X and Y are Banach spaces, if ImF′(x 0) ≠ Y. Otherwise, the mapping F is said to be regular.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 8, pp. 1097–1106, August, 2015.
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Prusińska, A., Tret’yakov, A. p-Regularity Theory. Tangent Cone Description in the Singular Case. Ukr Math J 67, 1236–1246 (2016). https://doi.org/10.1007/s11253-016-1148-y
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DOI: https://doi.org/10.1007/s11253-016-1148-y