PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

On certain weighted Schur type inequalities

Autorzy
Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this note we give sharp Schur type inequalities for univariate polynomials with convex weights. Our approach will rely on application of two-dimensional Markov type inequalities, and also certain properties of Jacobi polynomials in order to prove sharpness.
Rocznik
Strony
42--49
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
  • University of Applied Sciences in Tarnow, Faculty of Mathematics and Natural Sciences, Poland
Bibliografia
  • [1] Baran M. Markov inequality on sets with polynomial parametrization. Annales Polonici Mathematici. 1994;60(1):69–79.
  • [2] Baran M, Białas-Cież L. On the behaviour of constants in some polynomial inequalities. Annales Polonici Mathematici. 2019;123:43–60. https://doi.org/10.4064/ap180803-23-4.
  • [3] Beberok T. Lp Markov exponent of certain UPC sets. Zeitschrift fur Analysis und ihre Anwendungen. 2022;41(1/2):153–166. https://doi.org/10.4171/ZAA/1700.
  • [4] Białas-Cież L, Calvi J-P, Kowalska A. Polynomial inequalities on certain algebraic hypersurfaces. Journal of Mathematical Analysis and Applications. 2018;459(2):822–838. https://doi.org/10.1016/j.jmaa.2017.11.010.
  • [5] Białas-Cież L, Calvi J-P, Kowalska A. Markov and division inequalities on algebraic sets [preprint]. 2022;7.
  • [6] Białas-Cież L, Sroka G. Polynomial inequalities in Lp norms with generalized Jacobi weights. Mathematical Inequalities and Applications. 2019;22(1):261–274. https://dx.doi.org/10.7153/mia-2019-22-20.
  • [7] Borwein P, Erdélyi T. Polynomials and Polynomial Inequalities. New York, NY: Springer; 1995. https://doi.org/10.1007/978-1-4612-0793-1.
  • [8] Erdélyi T. Remez-type inequalities and their applications. Journal of Computational and Applied Mathematics. 1993;47(2):167–209.
  • [9] Joung H. Weighted inequalities for generalized polynomials with doubling weights. Journal of Inequalities and Applications. 2017:91. https://doi.org/10.1186/s13660-017-1369-0.
  • [10] Kroó A. Schur type inequalities for multivariate polynomials on convex bodies. Dolomites Research Notes on Approximation. 2017;10:15–22.
  • [11] Kroó A. Sharp Lp Markov type inequality for cuspidal domains in ℝd. Journal of Approximation Theory. 2020;250:105336. https://doi.org/10.1016/j.jat.2019.105336.
  • [12] Milovanović GV, Mitrinović DS, Rassias TM. Topics in Polynomials: Extremal Problems, Inequalities, Zeros. Singapore: World Scientic; 1994. https://doi.org/10.1142/1284.
  • [13] Pierzchała R. Polynomial inequalities, o-minimality and Denjoy-Carleman classes. Advances in Mathematics. 2022;407:108565. https://doi.org/10.1016/j.aim.2022.108565.
  • [14] Révész SG. Schur-Type inequalities for complex polynomials with no zeros in the unit disk. Journal of Inequalities and Applications. 2007:090526. https://doi.org/10.1155/2007/90526.
  • [15] Szegö G. Orthogonal Polynomials. Providence: American Mathematical Society; 1975.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-03c04fd3-c4c7-4fe5-897b-9dd18bcb7ea2
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.