New Inequalities on $L_{\gamma}$-Spaces

New Inequalities on $L_{\gamma}$-Spaces

Year:    2013

Analysis in Theory and Applications, Vol. 29 (2013), Iss. 4 : pp. 390–400

Abstract

We consider for a fixed $\mu$, the class of polynomials $$P_{n,\mu,s}:=\Bigg\{ P(z) =z^s(a_nz^{n−s}+ \sum^{n-s}_{j=\mu}a_{n−j}z^{n−j−s}); 1≤\mu≤n−s\Bigg\}$$ of degree $n$, having all zeros in $|z|≤k,$ $k≤1$, with $s$-fold zeros at the origin. In this paper, we have obtained inequalities in the reverse direction for the above class of polynomials. Besides, extensions of some Turan-type inequalities for the polar derivative of polynomials have been considered.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.2013.v29.n4.8

Analysis in Theory and Applications, Vol. 29 (2013), Iss. 4 : pp. 390–400

Published online:    2013-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    11

Keywords:    Polynomial Zygmund inequality polar derivative.

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