On an operator preserving inequalities between polynomials

• Datum: 2017
• Hauptverfasser: Mir, A., Мир, А.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2017
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/1758
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

Let $P(z)$ be a polynomial of degree n. We consider an operator $D\alpha$ that maps $P(z)$ into $D\alpha P(z) := nP(z)+(\alpha z)P\prime (z)$ and establish some results concerning the estimates of $| D\alpha P(z)| $ on the disk $| z| = R \geq 1$, and thereby obtain extensions and generalizations...