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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.
IMPROVED BOUNDS OF POLYNOMIAL INEQUALITIES WITH RESTRICTED ZERO
Robinson Soraisam,Nirmal Kumar Singha,Barchand Chanam 경남대학교 수학교육과 2023 Nonlinear Functional Analysis and Applications Vol.28 No.2
In this paper, we shall first improve as well as generalize the above inequality. Further, we also improve the bounds of two known inequalities obtained by Govil et al. [8].
INEQUALITIES FOR COMPLEX POLYNOMIAL WITH RESTRICTED ZEROS
Istayan Das,Robinson Soraisam,Mayanglambam Singhajit Singh,Nirmal Kumar Singha,Barchand Chanam 경남대학교 수학교육과 2023 Nonlinear Functional Analysis and Applications Vol.28 No.4
Let $p(z)$ be a polynomial of degree $n$ and for any complex number $\beta$, let $D_\beta p(z)=np(z)+(\beta-z)p^\prime(z)$ denote the polar derivative of the polynomial with respect to $\beta$. In this paper, we consider the class of polynomial$$p(z)=(z-z_{0})^s\left(a_{0}+\displaystyle{\sum_{\nu=0}^{n-s}a_{\nu}z^{\nu}}\right)$$ of degree $n$ having a zero of order $s$ at $z_0$, $|z_{0}|<1$ and the remaining $n-s$ zeros are outside $|z|<k$, $k\geq1$ and establish upper bound estimates for the maximum of $\left|D_\beta p(z)\right|$ as well as $\left|p(Rz)-p(rz)\right|$, $R\geq r\geq1$ on the unit disk.