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

LP−type inequalities for derivative of a polynomial

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Published: Dec 30, 2021
Keywords:
polynomial, derivative and Integral mean inequalities.
Mathematics Subject Classification:
26D10, 30C15, 41A17.

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Irfan Ahmad Wani
Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India
Mohammad Ibrahim Mir
Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India
Ishfaq Nazir
Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India

Abstract

For the polynomial P(z) of degree n and having all its zeros in |z|≤k, k≥1, Jain [6] proved that

max|z|=1|P′(z)|≥n|c0|+|cn|kn+1|c0|(1+kn+1)+|cn|(kn+1+k2n)max|z|=1|P(z)|.

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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