Construction of intermediate differentiable functions

  • V. K. Maslyuchenko
  • V. S. Mel'nik

Abstract

For given upper and lower semicontinuous real-valued functions $g$ and $h$, respectively, defined on a closed parallelepiped $X$ in $R^n$ and such that $g(x) < h(x)$ on $X$ and points $x_0 \in X$ and $y_0 \in (g(x_0), h(x_0))$, we construct a smooth function $f : X \rightarrow R$ such that $f(x_0) = y_0$ and $g(x) < f(x) < h(x)$ on $X$. We also present similar constructions for functions defined on separable Hilbert spaces and Asplund spaces.
Published
25.05.2018
How to Cite
MaslyuchenkoV. K., and Mel’nikV. S. “Construction of Intermediate Differentiable Functions”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, no. 5, May 2018, pp. 672-81, http://umj.imath.kiev.ua/index.php/umj/article/view/1586.
Section
Research articles