Geodesic
Jackson-type theorem on approximation by algebraic
Matematičeskie zametki, Tome 116 (2024) no. 1, pp. 34-44.

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I. I. Sharapudinov, when studying the approximation properties of partial sums of a special series in Laguerre polynomials, introduced a weighted best approximation characteristic $E_n(f,u_r)$ that depends on a parameter $r$. In the present paper, we prove a Jackson-type theorem for this characteristic for $r=1$.
Mots-clés : Laguerre polynomial
Keywords: special series, Vallée-Poussin mean, Sobolev-type inner product. 
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R. M. Gadzhimirzaev. Jackson-type theorem on approximation by algebraic. Matematičeskie zametki, Tome 116 (2024) no. 1, pp. 34-44. http://geodesic.mathdoc.fr/item/MZM_2024_116_1_a2/

[1] I. I. Sharapudinov, “Spetsialnye ryady po polinomam Lagerra i ikh approksimativnye svoistva”, Sib. matem. zhurn., 58:2 (2017), 440–467 | DOI | MR

[2] I. I. Sharapudinov, Z. D. Gadzhieva, R. M. Gadzhimirzaev, “Sistemy funktsii, ortogonalnykh otnositelno skalyarnykh proizvedenii tipa Soboleva s diskretnymi massami, porozhdennykh klassicheskimi ortogonalnymi sistemami”, Dagestanskie elektronnye matematicheskie izvestiya, 2016, no. 6, 31–60 | DOI

[3] I. Joó, N. X. Ký, “Answer to a problem of Paul Turán”, Ann. Univ. Sci. Budapest. Eötvös Sect. Math., 31 (1988), 229–241 | MR

[4] G. Mastroianni, J. Szabados, “Polynomial approximation on infinite intervals with weights having inner zeros”, Acta Math. Hungar., 96:3 (2002), 221–258 | DOI | MR

[5] G. Mastroianni, W. Themistoclakis, “De la Vallée Poussin means and Jackson's theorem”, Acta Sci. Math. (Szeged), 74:1–2 (2008), 147–170 | MR

[6] N. X. Ky, “On approximation of functions by polynomials with weight”, Acta Math. Hungar., 59:1-2 (1992), 49–58 | DOI | MR

[7] D. S. Lubinsky, V. Totik, “Best weighted polynomial approximation via Jacobi expansions”, SIAM J. Math. Anal., 25:2 (1994), 555–570 | DOI | MR

[8] V. M. Fedorov, “Priblizhenie algebraicheskimi mnogochlenami s vesom Chebysheva–Ermita”, Izv. vuzov. Matem., 1984, no. 6, 55–63 | MR | Zbl

[9] G. Sege, Ortogonalnye mnogochleny, Fizmatgiz, M., 1962 | MR

[10] R. M. Gadzhimirzaev, “Approksimativnye svoistva srednikh tipa Valle Pussena chastichnykh summ ryada Fure po polinomam Lagerra–Soboleva”, Sib. matem. zhurn., 63:3 (2022), 545–561 | DOI | MR

[11] S. M. Nikolskii, “Priblizhenie funktsii trigonometricheskimi polinomami v srednem”, Izv. AN SSSR. Ser. matem., 10:3 (1946), 207–256 | MR | Zbl

[12] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii, v. 2, Nauka, M., 1966 | MR