Abstract
Let G n be the set of all real algebraic polynomials of degree at most n, positive on the interval (−1, 1) and without zeros inside the unit circle (|z| < 1). In this paper an inequality for the polynomials from the set G n is obtained. In one special case this inequality is reduced to the inequality given by B. Sendov [5] and in another special case it is reduced to an inequality between uniform norm and norm in the L 2 space for the Jacobi weight.
Similar content being viewed by others
References
I. Dimovski and V. Čakalov, Integral inequalities for real polynomials, Annuaire Univ. Sofia Fac. Math., 59 (1964/65), 151–158 (in Bulgarian).
A. Lupas, An inequality for polynomials, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz., 461–497 (1974), 241–243.
I. Ž. Milovanović and M. A. Kovačević, An extremal problem for real algebraic polynomials, Numerical methods and applications: proceedings of the International Conference on Numerical Methods and Applications, Pub. House of the Bulgarian Academy of Sciences, 1989, 304–312.
D. S. Mitrinović and P. M. Vasić, Analytic inequalities, Springer, New York, 1970.
B. Sendov, An integral inequality for algebraic polynomials with only real zeros, Annuaire Univ. Sofia Fac. Sci. Phys. Math., 53 (1958/1959), 19–32 (in Bulgarian).
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by György Petruska
Rights and permissions
About this article
Cite this article
Kovačević, M.A., Milovanović, I.Ž. An extremal problem for real algebraic polynomials. Period Math Hung 67, 167–173 (2013). https://doi.org/10.1007/s10998-013-5527-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10998-013-5527-y