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, No. 12, 37-46 (2007)]. As corollaries of this principle, new inequalities for the coefficients and derivatives of polynomials satisfying certain conditions on two intervals are obtained. Simple proofs of some Lukashov's theorems on the derivatives of rational functions on several intervals are provided. Bibliography: 13 titles.
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机译:本文考虑了V. N. Dubinin和S. I. Kalmykov [Mat。 Sb。,198,No. 12,37-46(2007)]。作为该原理的推论,获得了在两个区间上满足一定条件的多项式的系数和导数的新不等式。提供了关于卢卡绍夫定理在几个区间上导数的一些定理的简单证明。参考书目:13种。
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