Ukrainian Mathematical Journal

, Volume 67, Issue 8, pp 1236–1246 | Cite as

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

  • A. Prusińska
  • A. Tret’yakov

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 : XY 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.


Banach Space Implicit Function Theorem Regularity Theory Singular Case Linear Manifold 
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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • A. Prusińska
    • 1
  • A. Tret’yakov
    • 1
    • 2
  1. 1.Siedlce University of Natural Sciences and HumanitiesSiedlcePoland
  2. 2.System Research InstitutePolish Academy of SciencesWarsawPoland

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