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An extremal problem for real algebraic polynomials

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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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Correspondence to Milan A. Kovačević.

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Communicated by György Petruska

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Kovačević, M.A., Milovanović, I.Ž. An extremal problem for real algebraic polynomials. Period Math Hung 67, 167–173 (2013). https://doi.org/10.1007/s10998-013-5527-y

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  • DOI: https://doi.org/10.1007/s10998-013-5527-y

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