On an operator preserving inequalities between polynomials - Mir, A. (Ukrains’kyi Matematychnyi Zhurnal, 2017)
Let $P(z)$ be a polynomial of degree n. We consider an operator $Dα$ that maps $P(z)$ into $Dα P(z) := nP(z)+(α z)P′ (z)$and establish some results concerning the estimates of $| Dα P(z)| $ on the disk $| z| = R ≥ 1$, and thereby obtain extensionsand generalizations of a number of well-known polynomial inequalities.