Geodesic
Criteria for the constant sign property for real polynomials on a segment
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2008), pp. 80-85

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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. 
@article{IVM_2008_11_a7,
     author = {V. \`E. Gheit and N. Zh. Gheit},
     title = {Criteria for the constant sign property for real polynomials on a segment},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {80--85},
     publisher = {mathdoc},
     number = {11},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2008_11_a7/}
}
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V. È. Gheit; N. Zh. Gheit. Criteria for the constant sign property for real polynomials on a segment. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2008), pp. 80-85. http://geodesic.mathdoc.fr/item/IVM_2008_11_a7/