An extremal problem for polynomials with nonnegative coefficients
Author:
Gradimir V. Milovanović
Journal:
Proc. Amer. Math. Soc. 94 (1985), 423426
MSC:
Primary 26C05; Secondary 41A17
MathSciNet review:
787886
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Abstract: Let be the set of all algebraic polynomials of exact degree whose coefficients are all nonnegative. For the norm in with generalized Laguerre weight function , the extremal problem is solved, which completes a result of A. K. Varma [7].
 [1]
P.
Erdös, On extremal properties of the derivatives of
polynomials, Ann. of Math. (2) 41 (1940),
310–313. MR 0001945
(1,323g)
 [2]
G.
G. Lorentz, The degree of approximation by polynomials with
positive coefficients, Math. Ann. 151 (1963),
239–251. MR 0155135
(27 #5075)
 1.
G.
G. Lorentz, Derivatives of polynomials with positive
coefficients, J. Approximation Theory 1 (1968),
1–4. MR
0231957 (38 #283)
 [4]
A. A. Markov, On a problem of D. I. Mendeleev, Izv. Akad. Nauk SSSR Ser. Mat. 62 (1889), 124.
 [5]
Gábor
Szegö, On some problems of approximations, Magyar Tud.
Akad. Mat. Kutató Int. Közl. 9 (1964),
3–9 (English, with Russian summary). MR 0173895
(30 #4102)
 [6]
P.
Turán, Remark on a theorem of Erhard Schmidt,
Mathematica (Cluj) 2 (25) (1960), 373–378. MR 0132963
(24 #A2799)
 [7]
A.
K. Varma, Derivatives of polynomials with
positive coefficients, Proc. Amer. Math.
Soc. 83 (1981), no. 1, 107–112. MR 619993
(82j:26014), http://dx.doi.org/10.1090/S00029939198106199930
 [8]
A.
K. Varma, Some inequalities of algebraic
polynomials having real zeros, Proc. Amer.
Math. Soc. 75 (1979), no. 2, 243–250. MR 532144
(80k:28019), http://dx.doi.org/10.1090/S00029939197905321447
 [9]
A.
K. Varma, An analogue of some inequalities of P.
Turán concerning algebraic polynomials having all zeros inside
[1,+1], Proc. Amer. Math. Soc.
55 (1976), no. 2,
305–309. MR 0396878
(53 #738), http://dx.doi.org/10.1090/S00029939197603968787
 [10]
A.
K. Varma, An analogue of some inequalities of P.
Turán concerning algebraic polynomials having all zeros inside
[1,+1]. II, Proc. Amer. Math. Soc.
69 (1978), no. 1,
25–33. MR
0473124 (57 #12802), http://dx.doi.org/10.1090/S00029939197804731249
 [1]
 P. Erdös, Extremal properties of derivatives of polynomials, Ann. of Math. (2) 41 (1940), 310313. MR 0001945 (1:323g)
 [2]
 G. G. Lorentz, The degree of approximation by polynomials with positive coefficients, Math. Ann. 151 (1963), 239251. MR 0155135 (27:5075)
 1.
 , Derivatives of polynomials with positive coefficients, J. Approx. Theory 1 (1968), 14. MR 0231957 (38:283)
 [4]
 A. A. Markov, On a problem of D. I. Mendeleev, Izv. Akad. Nauk SSSR Ser. Mat. 62 (1889), 124.
 [5]
 G. Szegö, On some problems of approximations, Magyar Tud. Akad. Mat. Kutato Int. Dozl. 2 (1964), 39. MR 0173895 (30:4102)
 [6]
 P. Turan, Remarks on a theorem of Erhard Schmidt, Mathematica (2) 25 (1960), 373378. MR 0132963 (24:A2799)
 [7]
 A. K. Varma, Derivatives of polynomials with positive coefficients, Proc. Amer. Math. Soc. 83 (1981), 107112. MR 619993 (82j:26014)
 [8]
 , Some inequalities of algebraic polynomials having real zeros, Proc. Amer. Math. Soc. 75 (1979), 243250. MR 532144 (80k:28019)
 [9]
 , An analogue of some inequalities of P. Turan concerning algebraic polynomials having all zeros inside , Proc. Amer. Math. Soc. 55 (1976), 305309. MR 0396878 (53:738)
 [10]
 , An analogue of some inequalities of P. Turan concerning algebraic polynomials having all zeros inside . II, Proc. Amer. Math. Soc. 69 (1978), 2533. MR 0473124 (57:12802)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198507878868
PII:
S 00029939(1985)07878868
Article copyright:
© Copyright 1985
American Mathematical Society
