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 extensions and generalizations of a number of well-known polynomial inequalities.