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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, Number 11, Pages 80–85 (Mi ivm1779)  
Criteria for the constant sign property for real polynomials on a segment

V. È. Gheit, N. Zh. Gheit

Chelyabinsk State University
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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
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2008, Volume 52, Issue 11, Pages 70–75
DOI: https://doi.org/10.3103/S1066369X0811008X
Bibliographic databases:
UDC: 517.518
Language: Russian
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
Citation in format AMSBIB
\Bibitem{GheGhe08}
\by V.~\`E.~Gheit, N.~Zh.~Gheit
\paper Criteria for the constant sign property for real polynomials on a segment
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2008
\issue 11
\pages 80--85
\mathnet{http://mi.mathnet.ru/ivm1779}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2530587}
\zmath{https://zbmath.org/?q=an:1173.26311}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2008
\vol 52
\issue 11
\pages 70--75
\crossref{https://doi.org/10.3103/S1066369X0811008X}
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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