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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.
Czasopismo
Rocznik
Tom
Strony
42--49
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
autor
- 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.
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Bibliografia
Identyfikator YADDA
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