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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Besides, our results are also found to generalize and improve some known inequalities.
📌 3 Key Takeaways
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Objective & Hypothesis:Let $P(z)=a_0+\sum\limits_{\nu=\mu}^na_{\nu}z^{\nu}$, $1\leq\mu\leq n$, be a polynomial of degree $n$ having all its zeros in $|z|\leq k$, $k\geq 1$.
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Key Findings & Data:We obtain an improvement and a generalization of an inequality in polar derivative proved by Somsuwan and Nakprasit [1].
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Conclusion & Impact:Besides, our results are also found to generalize and improve some known inequalities.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Turan type inequality · Polynomial · Polar Derivative
Abstract
Let $P(z)=a_0+\sum\limits_{\nu=\mu}^na_{\nu}z^{\nu}$, $1\leq\mu\leq n$, be a polynomial of degree $n$ having all its zeros in $|z|\leq k$, $k\geq 1$. We obtain an improvement and a generalization of an inequality in polar derivative proved by Somsuwan and Nakprasit [1]. Further, we also extend a result proved by Chanam and Dewan [2] to its polar version. Besides, our results are also found to generalize and improve some known inequalities.
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Cite This Article
KRİSHNADAS, K., SİNGH, T., CHANAM, B. (2023). Generalized Turan-type Inequalities for Polar Derivative of a Polynomial. Mathematical Sciences and Applications E-Notes, Cilt: 11 Sayı: 4, 178–191. https://ajindex.com/articles/967678