Far Eastern Mathematical Journal

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On polynomials normalized on an interval


Kalmykov S.I.

2018, issue 2, Ñ. 261-266


Abstract
In this short communication new covering theorems, two-point distortion theorems and coefficient estimates for polynomials with a curved majorant on an interval are presented. Extremal polynomials in these therems are Chebyshev polynomials of the the second, third and forth kinds. Proofs are based on a new version of the Schwarz lemma and a univalent condition for holomorphic functions suggested by Dubinin.

Keywords:
Chebyshev polynomials, Bernstein inequality, conformal mappings

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References

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