Some inequalities of algebraic polynomials with nonnegative coefficients
Author:
Weiyu Chen
Journal:
Trans. Amer. Math. Soc. 347 (1995), 21612167
MSC:
Primary 41A17
MathSciNet review:
1273483
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Abstract: Let be the collection of all algebraic polynomials of degree with nonnegative coefficients. In this paper we discuss the extremal problem where is a positive and integrable function. This problem is solved completely in the cases The second case was solved by Varma for some values of and by Milovanović completely. We provide a new proof here in this case.
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, Some inequalities of algebraic polynomials, preprint.
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 P. Dörfler, New inequalities of Markov type, SIAM J. Math. Anal. 18 (1987), 490494. MR 876288 (88f:41024)
 [2]
 , An extremal problem concerning a Markovtype inequality, SIAM J. Math. Anal. 22 (1991), 792795. MR 1091682 (91k:41024)
 [3]
 G. G. Lorentz, Degree of approximation by polynomials with positive coefficients, Math. Ann. 151 (1963), 239251. MR 0155135 (27:5075)
 [4]
 G. V. Milovanović, An extremal problem for polynomials with nonnegative coefficients, Proc. Amer. Math. Soc. 94 (1985), 423426. MR 787886 (86g:26020)
 [5]
 G. V. Milovanović and M. S. Petković, Extremal problems for Lorentz classes of nonnegative polynomials in metric with Jacobi weight, Proc. Amer. Math. Soc. 102 (1988), 283289. MR 920987 (88k:26016)
 [6]
 L. Mirsky, An inequality of the MarkovBernstein type for polynomials, SIAM J. Math. Anal. 14 (1983), 10041008. MR 711180 (84h:41030)
 [7]
 J. T. Scheick, Inequalities for derivatives of polynomials of special type, J. Approx. Theory 6 (1972), 354358. MR 0342909 (49:7653)
 [8]
 P. Turán, Remark on a theorem of Erhard Schmidt, Mathematica 2 (1960), 373378. MR 0132963 (24:A2799)
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 A. K. Varma, Some inequalities of algebraic polynomials having real zeros, Proc. Amer. Math. Soc. 75 (1979), 243250. MR 532144 (80k:28019)
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 , Derivatives of polynomials with positive coefficients, Proc. Amer. Math. Soc. 83 (1981), 107112. MR 619993 (82j:26014)
 [11]
 , Some inequalities of algebraic polynomials, preprint.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947199512734838
PII:
S 00029947(1995)12734838
Keywords:
Markov inequality,
nonnegative coefficients
Article copyright:
© Copyright 1995
American Mathematical Society
