LP−TYPE INEQUALITIES FOR DERIVATIVE OF A POLYNOMIAL
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초록
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.
Abstract
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.
참고문헌 (12)
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