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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
Article

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.

Keywords

Banach Space Implicit Function Theorem Regularity Theory Singular Case Linear Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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