Journal of Mathematical Sciences

, Volume 157, Issue 4, pp 623–631 | Cite as

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


The paper considers the equality cases in the rnajoration 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.


Russia Rational Function Apply Mathematic Meromorphic Function Simple Proof 
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Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.Institute of Applied MathematicsFar-Eastern Branch of the Russian Academy of SciencesVladivostockRussia

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