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

  • A. Prusińska
  • A. Tret’yakov

Abstract

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.
Published
25.08.2015
How to Cite
PrusińskaA., and Tret’yakovA. “$p$-Regularity Theory. Tangent Cone Description in the Singular Case”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, no. 8, Aug. 2015, pp. 1097-06, http://umj.imath.kiev.ua/index.php/umj/article/view/2048.
Section
Research articles