• Korean Journal of Mathematics
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• v.29 no.2
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• pp.435-443
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• 2021

In this paper, we consider an operator N : 𝓟_n → 𝓟_n on the space of polynomials 𝓟_n of degree at most n and establish some compact generalizations of Bernstein-type polynomial inequalities, which include several well known polynomial inequalities as special cases.

• Korean Journal of Mathematics
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• v.30 no.2
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• pp.231-238
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• 2022

In this paper we prove some results by using a simple but elegant techniques to improve and strengthen some generalizations and refinements of two widely known polynomial inequalities and thereby deduce some useful corollaries.

• Korean Journal of Mathematics
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• v.28 no.4
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• pp.931-942
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• 2020

For a polynomial $P(z)={\sum_{{\nu}=0}^{n}}\;a_{\nu}z^{\nu}$ of degree n having all its zeros in |z| ≤ k, k ≥ 1, it was shown by Rather and Dar [13] that ${\max_{{\mid}z{\mid}=1}}{\mid}P^{\prime}(z){\mid}{\geq}{\frac{1}{1+k^n}}\(n+{\frac{k^n{\mid}a_n{\mid}-{\mid}a_0{\mid}}{k^n{\mid}a_n{\mid}+{\mid}a_0{\mid}}}\){\max_{{\mid}z{\mid}=1}}{\mid}P(z){\mid}$. In this paper, we shall obtain some sharp estimates, which not only refine the above inequality but also generalize some well known Turán-type inequalities.