Abstract
An inverse theorem for the best weighted polynomial approximation of a function in\(L_{w_\alpha }^p \) (S) is established. We also investigate Besov spaces generated by Freud weight and their connection with algebraic polynomial approximation in\(L_p (R)_{W_\lambda } \), wherew α is a Jacobi-type weight onS, 0<p ≤ ∞,S is a simplex andW λ is a Freud weight. For Ditzian-TotikK-functionals onL p(S), 1 ≤p ≤ ∞, we obtain a new equivalence expression.
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References
Z Ditzian, V Totik. Moduli of Smoothness. New York: Springer-Verlag, 1987
Z Ditzian, D Jiang, D Leviatan. Inverse theorem for best polynomial approximation inL p, 0<p<1. Proc Amer Math Soc, 1994, 120(1): 151–154
H Berens, Y Xu.K-moduli, moduli of smoothness, and Berenstein polynomials on a simplex. Indag Mathem N S 1991, 2(3): 411–421
Z Ditzian, X Zhou. Optimal approximation class for multivariate Bernstein operators. Pacific Jour of Math, 1993, 158(1): 93–120
H Berens, H J Schmid, Y Xu. Bernstein-Durrmeyer polynomial on a simplex. J Approx Theory, 1992, 68(3): 240–261
W Chen, Z Ditzian. Best polynomial and Durrmeyer approximation inL p(S). Indag Mathem N S, 1991, 2(4): 437–452
Song Li. Bernstein-Kantorovich operators on a simplex. Chinese J Approx Theory Appl, 11(3): 11–21
Z Ditzian, V H Hristov, K G Ivanov. Moduli of smoothness andK-functionals inL p, 0<p<1. Constr Approx, 1995, 11(1): 67–83
Z Ditzian, D S Lubinsky. Jackson and smoothness theorems for Freud weights inL p(0<p ≤ ∞). Constr Approx, 1997, 13(1): 99–151
Z Ditzian, V Totik. Remarks on Besov spaces and best polynomial approximation. Proc Amer Math Soc, 1988, 104(4): 1059–1066
Song Li. The equivalence relations between the Ditzian-Totik moduli of smoothness and best polynomial approximation in the Besov spaces. J Math Anal Appli, 1997, 215(1): 1–14.
R A Devore, X M Yu.K-functionals for Besov spaces. J Approx Theory, 1991, 67(1): 38–50
Song Li. The characterization of the best approximation, best approximation elements and a kind of linear operators in the Besov type spaces. Acta Math Sinica, 1997, 13(4): 527–536
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Li, S. K-functional, weighted moduli of smoothness, and best weighted polynomial approximation on a simplex. Acta Mathematica Sinica 15, 395–406 (1999). https://doi.org/10.1007/BF02650734
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DOI: https://doi.org/10.1007/BF02650734