On an operator preserving inequalities between polynomials

  • A. Mir


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 of a number of well-known polynomial inequalities.
How to Cite
Mir, A. “On an Operator Preserving Inequalities Between Polynomials”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, no. 8, Aug. 2017, pp. 1061-72, https://umj.imath.kiev.ua/index.php/umj/article/view/1758.
Research articles