Year: 2015
Analysis in Theory and Applications, Vol. 31 (2015), Iss. 1 : pp. 81–91
Abstract
Let P(z) be a polynomial of degree n having all its zeros in |z|≤k. For k=1, it is known that for each r>0 and |α|≥1, n(|α|−1){∫2π0|P(eiθ)|rdθ}1r≤{∫2π0|1+eiθ|rdθ}1rmax|z|=1|DαP(z)|. In this paper, we shall first consider the case when k≥1 and present certain generalizations of this inequality. Also for k≤1, we shall prove an interesting result for Lacunary type of polynomials from which many results can be easily deduced.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2015.v31.n1.7
Analysis in Theory and Applications, Vol. 31 (2015), Iss. 1 : pp. 81–91
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: Polynomial zeros polar derivative.