http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
IMPROVED VERSION ON SOME INEQUALITIES OF A POLYNOMIAL
Rashmi Rekha Sahoo,N. Reingachan,Robinson Soraisam,Khangembam Babina Devi,Barchand Chanam 경남대학교 수학교육과 2023 Nonlinear Functional Analysis and Applications Vol.28 No.4
Let $P(z)$ be a polynomial of degree $n$ and $P(z)\neq0$ in $|z|<1$. Then for every real $\alpha$ and $R>1$,Aziz \cite{Aziz1} proved that$$ \max_{|z|=1}|P(Rz)-P(z)|\leq \frac{R^{n}-1}{2}\left(M_{\alpha}^{2}+M_{\alpha+\pi}^{2}\right)^{\frac{1}{2}},$$where\begin{equation*}M_{\alpha}=\max_{1\leq k\leq n}|P(e^{i(\alpha+2k\pi) n})|. \end{equation*}\par In this paper, we establish some improvements and generalizations of the above inequality concerning the polynomials and their ordinary derivatives.