多项式的Bernstein和Turán-type不等式的锐化

Journal of classical analysis Pub Date : 2021-01-01 DOI:10.7153/jca-2021-18-10

Thangjam Birkramjit Singh, Maisnam Triveni Devi, B. Chanam

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引用次数: 1

摘要

．设p (z)是n次多项式。Govil和Mctume [Acta Math. 104, 115-126(2004)]定义了p (z)对实数或复数α的极坐标导数，证明了如果p是具有其全部| | 1的a，则对于任意复数α，本文证明了对上述不等式的改进。此外，我们还证明了Govil [Proc. Natl]对结果的改进。学会科学。， 50, 50 - 52(1980)]。

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Sharpening of Bernstein and Turán-type inequalities for polynomials

. Let p ( z ) be a polynomial of degree n . The polar derivative of p ( z ) with respect to a real or complex number α is de ﬁ ned by Govil and Mctume [Acta Math. 104, 115–126 (2004)] proved that if p is a of having all its | | 1, then for any complex number α with In this paper, we prove an improvement of the above inequality. Further, we prove an improve- ment of a result due to Govil [Proc. Natl. Acad. Sci., 50, 50–52 (1980)].

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