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http://dx.doi.org/10.11568/kjm.2021.29.4.775

LP-TYPE INEQUALITIES FOR DERIVATIVE OF A POLYNOMIAL  

Wani, Irfan Ahmad (Department of Mathematics, University of Kashmir, South Campus)
Mir, Mohammad Ibrahim (Department of Mathematics, University of Kashmir, South Campus)
Nazir, Ishfaq (Department of Mathematics, University of Kashmir, South Campus)
Publication Information
Korean Journal of Mathematics / v.29, no.4, 2021 , pp. 775-784 More about this Journal
Abstract
For the polynomial P(z) of degree n and having all its zeros in |z| ≤ k, k ≥ 1, Jain [6] proved that $${{\max\limits_{{\mid}z{\mid}=1}}\;{\mid}P^{\prime}(z){\mid}{\geq}n\;{\frac{{\mid}c_0{\mid}+{\mid}c_n{\mid}k^{n+1}}{{\mid}c_0{\mid}(1+k^{n+1})+{\mid}c_n{\mid}(k^{n+1}+k^{2n})}\;{\max\limits_{{\mid}z{\mid}=1}}\;{\mid}P(z){\mid}$$. 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.
Keywords
polynomial; derivative and Integral mean inequalities;
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