On a property of the arithmetic means of monotonous sequences

• Datum: 2022
• Hauptverfasser: Korenovskyi, A. O., Shanin, R. V., Кореновський, А. О., Шанiн, Р. В.
• Format: Artikel
• Sprache: Ukrainisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2022
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/7151
• Назва журналу: 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...