Construction of intermediate differentiable functions

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


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.
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,
Research articles