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Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2022 / Cilt: 71 - Sayı: 3

On the maximum modulus of a complex polynomial

Shabir MALİK
Ashish KUMAR
Sayfa
666–681
Yayın Tarihi
2022-09-30
DOI
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Moreover, the problem of estimating p(1−wn)p(1−wn), $0<w\leq$ given $p(1)=0$ is considered.

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Amaç & Hipotez:In this paper we impose distinct restrictions on the moduli of the zeros of p(z)=n∑v=0avzvp(z)=∑v=0navzv and investigate the dependence of ∥p(Rz)−p(σz)∥‖p(Rz)−p(σz)‖, R>σ≥1R>σ≥1 on MαMα and Mα+πMα+π, where Mα=max1≤k≤n|p(ei(α+2kπ)/n)|Mα=max1≤k≤n|p(ei(α+2kπ)/n)| and on certain coefficients of p(z)p(z).
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Temel Bulgular & Veri:This paper comprises several results, which in particular yields some classical polynomial inequalities as special cases.
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Sonuç & Katkı:Moreover, the problem of estimating p(1−wn)p(1−wn), $0<w\leq$ given $p(1)=0$ is considered.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Polynomials · definite integral · zeros

Abstract

In this paper we impose distinct restrictions on the moduli of the zeros of p(z)=n∑v=0avzvp(z)=∑v=0navzv and investigate the dependence of ∥p(Rz)−p(σz)∥‖p(Rz)−p(σz)‖, R>σ≥1R>σ≥1 on MαMα and Mα+πMα+π, where Mα=max1≤k≤n|p(ei(α+2kπ)/n)|Mα=max1≤k≤n|p(ei(α+2kπ)/n)| and on certain coefficients of p(z)p(z). This paper comprises several results, which in particular yields some classical polynomial inequalities as special cases. Moreover, the problem of estimating p(1−wn)p(1−wn), $0<w\leq$ given $p(1)=0$ is considered.

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Bu Makaleye Atıf Yap

MALİK, S., KUMAR, A. (2022). On the maximum modulus of a complex polynomial. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Cilt: 71 - Sayı: 3, 666–681. https://ajindex.com/articles/746623

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Kaynakça (16)

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