Construction of intermediate differentiable functions

• Date: 2018
• Main Authors: Maslyuchenko, V. K., Mel'nik, V. S., Маслюченко, В. К., Мельник, В. С.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2018
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1586
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...