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For the polynomial $P(z)$ of degree $n$ and having all its zeros in $|z| \leq k$, $k \geq 1$, Jain \cite{j} proved that \begin{align*} \max_{|z|=1} |P^{\prime}(z)|\geq n \frac{|c_0| + |c_n|k^{n+1}}{|c_0|(1+k^{n+1}) + |c_n| ( k^{n+1} + k^{2n})} \max_{|z|=1}|P(z)| .
\end{align*} In this paper, we extend above inequality to its integral analogous and there by obtain more results which extended the already proved results to integral analogous.
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참고문헌 (12)
참고문헌 신청
A. Aziz / 1988 / Integral mean estimates for polynomials with restricted zeros / J. Approx 55:232~238
S. Bernstein / 1912 / Sur ´e ordre de la meilleure approximation des functions continues par des poly-nomes de degr´e donn´e / Mem. Acad. R. Belg 4:1~103
N. K. Govil / 1973 / On the derivative of a polynomial / Proc. Amer. Math. Soc. 41:543~546
N. K. Govil / 1991 / Some inequalities for derivatives of polynomials / J. Approx. Theory 66:29~35
G. H. Hardy / 1915 / The mean value of the modulus of an analytic function / Proc. London Math. Soc 14:319~330
S. Bernstein / 1912 / Sur ´e ordre de la meilleure approximation des functions continues par des poly-nomes de degr´e donn´e / Mem. Acad. R. Belg 4:1~103
N. K. Govil / 1973 / On the derivative of a polynomial / Proc. Amer. Math. Soc. 41:543~546
N. K. Govil / 1991 / Some inequalities for derivatives of polynomials / J. Approx. Theory 66:29~35
G. H. Hardy / 1915 / The mean value of the modulus of an analytic function / Proc. London Math. Soc 14:319~330
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