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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Moreover, the problem of estimating p(1−wn)p(1−wn), $0<w\leq$ given $p(1)=0$ is considered.
📌 3 Key Takeaways
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Objective & Hypothesis: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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Key Findings & Data:This paper comprises several results, which in particular yields some classical polynomial inequalities as special cases.
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Conclusion & Impact:Moreover, the problem of estimating p(1−wn)p(1−wn), $0<w\leq$ given $p(1)=0$ is considered.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables: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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Cite This Article
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