An extremal problem for real algebraic polynomials |
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Authors: | Milan A. Kovačević Igor Ž. Milovanović |
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Affiliation: | 1. Faculty of Electronic Engineering, Department of Mathematics, University of Ni?, Aleksandra Medvedeva 14, P.O. Box 73, 18000, Ni?, Serbia
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Abstract: | 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. |
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