Multiple modules of continuity and the best approximations of periodic functions in metric spaces

• Datum: 2018
• Hauptverfasser: Pichugov, S. A., Пичугов, С. А.
• Format: Artikel
• Sprache: Russisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2018
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/1588
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

It is proved that, under the condition $M_{\Psi} \Bigl( \frac 12\Bigr) < 1$, where $M_{\Psi}$ is a stretching function $\Psi$ in the space $L_{\Psi}$ , the Jackson inequalities $$\sup_n \sup_{f\in L_{\Psi}, f\not = \text{const}} \frac{E_{n-1}(f)_{\Psi} }{\omega_k \Bigl(f, \frac{\pi}n \Bigr...