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http://dx.doi.org/10.22771/nfaa.2022.27.04.08

SOME INEQUALITIES ON POLAR DERIVATIVE OF A POLYNOMIAL  

N., Reingachan (Department of Mathematics, National Institute of Technology Manipur)
Robinson, Soraisam (Department of Mathematics, National Institute of Technology Manipur)
Barchand, Chanam (Department of Mathematics, National Institute of Technology Manipur)
Publication Information
Nonlinear Functional Analysis and Applications / v.27, no.4, 2022 , pp. 797-805 More about this Journal
Abstract
Let P(z) be a polynomial of degree n. A well-known inequality due to S. Bernstein states that if P ∈ Pn, then $$\max_{{\mid}z{\mid}=1}\,{\mid}P^{\prime}(z){\mid}\,{\leq}n\,\max_{{\mid}z{\mid}=1}\,{\mid}P(z){\mid}$$. In this paper, we establish some extensions and refinements of the above inequality to polar derivative and some other well-known inequalities concerning the polynomials and their ordinary derivatives.
Keywords
Inequalities; polynomials; zeros; polar derivative;
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