Theorems about intermediate affine function for convex and concave functions
1 Department of Mathematical Analysis, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine
2 Department of Mathematical Modeling, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine
Keywords:
affine function
Abstract
Given a convex set $E ⊆ \mathbb{R}$, we obtain different conditions that imply the existence of an such affine function $f: E→ \mathbb{R}$ such that $g(x) ≤ f(x) ≤ h(x)$ for all $x ∈ E$ and for every convex upward and convex downward functions $g,h: E→ \mathbb{R}$ possessing the inequality $g(x) ≤ h(x)$ for all $x ∈ E$.
Cite
- ACS Style
- Maslyuchenko, V.K.; Melnyk, V. Theorems about intermediate affine function for convex and concave functions. Bukovinian Mathematical Journal. 2016, 4
- AMA Style
- Maslyuchenko VK, Melnyk V. Theorems about intermediate affine function for convex and concave functions. Bukovinian Mathematical Journal. 2016; 4(1-2).
- Chicago/Turabian Style
- Volodymyr Kyrylovych Maslyuchenko, Vasyl Melnyk. 2016. "Theorems about intermediate affine function for convex and concave functions". Bukovinian Mathematical Journal. 4 no. 1-2.
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