$p$-Regularity Theory. Tangent Cone Description in the Singular Case
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 Im $F′(x_0) ≠ Y$. Otherwise, the mapping $F$ is said to be regular.
English version (Springer): Ukrainian Mathematical Journal 67 (2015), no. 8, pp 1236-1246.
Citation Example: Prusińska A., Tret’yakov A. $p$-Regularity Theory. Tangent Cone Description in the Singular Case // Ukr. Mat. Zh. - 2015. - 67, № 8. - pp. 1097-1106.