An extremal problem for real algebraic polynomials

Let G n be the set of all real algebraic polynomials of degree at most n, positive on the interval (−1, 1) and without zeros inside the unit circle (| z | < 1). In this paper an inequality for the polynomials from the set G n is obtained. In one special case this inequality is reduced to the ineq...

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Bibliographic Details
Published in:Periodica mathematica Hungarica 2013-12, Vol.67 (2), p.167-173
Main Authors: Kovačević, Milan A., Milovanović, Igor Ž.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:Let G n be the set of all real algebraic polynomials of degree at most n, positive on the interval (−1, 1) and without zeros inside the unit circle (| z | < 1). In this paper an inequality for the polynomials from the set G n is obtained. In one special case this inequality is reduced to the inequality given by B. Sendov [5] and in another special case it is reduced to an inequality between uniform norm and norm in the L 2 space for the Jacobi weight.
ISSN:0031-5303
1588-2829
DOI:10.1007/s10998-013-5527-y