Inequalities Concerning the Maximum Modulus of Polynomials
Year: 2018
Analysis in Theory and Applications, Vol. 34 (2018), Iss. 2 : pp. 175–186
Abstract
Let P(z) be a polynomial of degree n having all its zeros in |z|≤k, k≤1, then
for every real or complex number β, with |β|≤1 and R≥1, it was shown by A. Zireh et
al. [7] that for |z|=1,
min|z|=1|P(Rz)+β(R+k1+k)nP(z)|≥k−n|Rn+β(R+k1+k)n|min|z|=k|P(z)|.
In this paper, we shall present a refinement of the above inequality. Besides, we shall
also generalize some well-known results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2018.v34.n2.7
Analysis in Theory and Applications, Vol. 34 (2018), Iss. 2 : pp. 175–186
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Growth of polynomials minimum modulus of polynomials inequalities.