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L^r INEQUALITIES FOR POLYNOMIALS
Reingachan Ngamchui,M. S. Singh,N. K. Singha,K. B. Devi,B. Chanam 경남대학교 수학교육과 2024 Nonlinear Functional Analysis and Applications Vol.29 No.2
In this paper, we not only obtain the $L^{r}$ version of the polar derivative of the above inequality for $r>0$, but also obtain an improved $L^{r}$ extension in polar derivative.
IMPROVEMENT AND GENERALIZATION OF POLYNOMIAL INEQUALITY DUE TO RIVLIN
Nirmal Kumar Singha,Reingachan Ngamchui,Maisnam Triveni Devi,Barchand Chanam 경남대학교 수학교육과 2023 Nonlinear Functional Analysis and Applications Vol.28 No.3
Let $p(z)$ be a polynomial of degree $n$ having no zero in $\vert z\vert<1$. In this paper, by involving some coefficients of the polynomial, we prove an inequality that not only improves as well as generalizes the well-known result proved by Rivlin but also has some interesting consequences.
ON AN INEQUALITY OF S. BERNSTEIN
Barchand Chanam,Khangembam Babina Devi,Kshetrimayum Krishnadas,Maisnam Triveni Devi,Reingachan Ngamchui,Thangjam Birkramjit Singh 경남대학교 수학교육과 2021 Nonlinear Functional Analysis and Applications Vol.26 No.2
If $p(z)=\sum\limits_{\nu=0}^na_{\nu}z^{\nu}$ is a polynomial of degree $n$ having all its zeros on $|z|=k$, $k\leq 1$, then Govil [3]proved that\begin{align*}\max\limits_{|z|=1}|p'(z)|\leq \dfrac{n}{k^n+k^{n-1}}\max\limits_{|z|=1}|p(z)|. \end{align*} In this paper, by involving certain coefficients of $p(z)$, we not only improve the above inequality but also improve a result provedby Dewan and Mir [2].