On a property of the arithmetic means of monotonous sequences

• Date: 2022
• Main Authors: Korenovskyi, A. O., Shanin, R. V., Кореновський, А. О., Шанiн, Р. В.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2022
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/7151
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.5 For a sequence $Y = \{y_i\}_{i=P+1}^Q$ (the numbers $P, Q \in \mathbb Z$ are fixed, $P < Q$), we consider the arithmetic mean oscillations\begin{equation*}\Omega \big (Y;[p,q] \big )=\frac1{q-p}\sum\limits _{i=p+1}^q\left|y_i-\sigma \big (Y;[p,q] \big )\right|\!,\end{equation*}w...