References
P. Erdős, Extremal properties of polynomials, Ann. of Math., 4 (1940), 310–313.
P. Erdős and A. K. Varma, An extremum problem concerning algebraic polynomials, Acta. Math. Hungar., 47 (1986), 137–143.
J. Erőd, Bizonyos polinomok maximumának alsó korlátjáról (in Hungarian), Math. Fiz. Lapok, 46 (1939), 58–82.
E. Hille, G. Szegő and J. D. Tamarkin, On some generalizations of a theorem of A. A. Markov, Duke Math. Journal, 3 (1937), 729–739.
G. G. Lorentz, The degree of approximation by polynomials with positive coefficients, Math. Ann., 151 (1963), 239–251.
G. V. Milovanović and M. S. Petković, Extremal problems for Lorentz classes of nonnegative polynomials in L 2 metric with Jacobi weight, Proc. Amer. Math. Soc., 102 (1988), 283–289.
P. Turán, Über die Ableitung von Polynomen, Compositio Math., 7 (1939), 89–95.
A. K. Varma, An analogue of some inequalities of P. Erdős and P. Turán concerning algebraic polynomials satisfying certain conditions, Colloquia Mathematica Societatis János Bolyai, 19, Fourier Analysis and Approximation Theory, Budapest (1976).
A. K. Varma, Some inequalities of algebraic polynomials having all zeros inside [-1, 1], Proc. Amer. Math. Soc., 88 (1983), 227–233.
A. K. Varma, Some inequalities of algebraic polynomials having real zeros, Proc. Amer. Math. Soc., 75 (1979), 243–250.
S. P. Zhou, On Turán's inequality in the L pnorm (in Chinese), J. Hangzhou Univ., 11 (1984), 28–33.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Underhill, B., Varma, A.K. An extension of some inequalities of P. Erdős and P. Turán concerning algebraic polynomials. Acta Math Hung 73, 1–28 (1996). https://doi.org/10.1007/BF00058939
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00058939