Majoration principles and some inequalities for polynomials and rational functions with prescribed poles

The paper considers the equality cases in the majoration principle for meromorphic functions established earlier by V. N. Dubinin and S. I. Kalmykov [Mat. Sb. 198:12 (2007), 37–46; translated in Sb. Math. 198:11–12 (2007), 1737–1745]. As corollaries of this principle, we obtain new inequalities for the coefficients and derivatives of polynomials satisfying certain conditions on two intervals. Simple proofs of some Lukashov's theorems on the derivatives of rational functions on several intervals [MR 2069196 (2006):26010)] are provided. Bibl. – 13 titles.