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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, Number 11, Pages 80–85
(Mi ivm1779)
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Criteria for the constant sign property for real polynomials on a segment
V. È. Gheit, N. Zh. Gheit Chelyabinsk State University
Abstract:
It is well known that classic theorems of Markov and Lukach for real polynomials which have a constant sign on a segment are ineffective. In this paper we obtain criteria for the constant sign property on a segment for real polynomials of the fourth degree and formulate certain generalizations of them. The mentioned criteria are stated in terms of the coefficients of the polynomials under consideration.
Keywords:
nonnegative, nonpositive polynomials, polynomials with the least deviation from zero in the integral metric.
Received: 04.06.2008
Citation:
V. È. Gheit, N. Zh. Gheit, “Criteria for the constant sign property for real polynomials on a segment”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 11, 80–85; Russian Math. (Iz. VUZ), 52:11 (2008), 70–75
Linking options:
https://www.mathnet.ru/eng/ivm1779 https://www.mathnet.ru/eng/ivm/y2008/i11/p80
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Abstract page: | 311 | Full-text PDF : | 74 | References: | 48 | First page: | 2 |
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