TY - JOUR AU - V. K. Maslyuchenko AU - V. S. Mel'nik PY - 2018/05/25 Y2 - 2024/03/29 TI - Construction of intermediate differentiable functions JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 70 IS - 5 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/1586 AB - 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 functionsdefined on separable Hilbert spaces and Asplund spaces. ER -