Korean J. Math. Vol. 29 No. 4 (2021) pp.775-784
DOI: https://doi.org/10.11568/kjm.2021.29.4.775

$L_P-$type inequalities for derivative of a polynomial

Main Article Content

Irfan Ahmad Wani
Mohammad Ibrahim Mir
Mohammad Ibrahim Mir
Ishfaq Nazir
Ishfaq Nazir

Abstract

For the polynomial $P(z)$ of degree $n$ and having all its zeros in $|z| \leq k$, $k \geq 1$, Jain [6] 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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