p-Regularity Theory. Tangent Cone Description in the Singular Case

• Published in: Український математичний журнал
• Date: 2015
• ISSN: 1027-3190
• Main Authors: Prusińska, A., Tret’yakov, A.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2015
• Subjects: Статті
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/165760
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: p-Regularity Theory. Tangent Cone Description in the Singular Case / A. Prusińska, A. Tret’yakov // Український математичний журнал. — 2015. — Т. 67, № 8. — С. 1097–1106. — Бібліогр.: 7 назв. — англ.

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 x₀, where X and Y are Banach spaces, if ImF′(x₀) ≠...