p-Regularity Theory. Tangent Cone Description in the Singular Case - Prusińska, A.; Tret’yakov, A. (Ukrains’kyi Matematychnyi Zhurnal, 2015)
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.