Abstract
We obtain sharp Jackson-Stechkin type inequalities on the sets L r2,ρ (ℝ) in which the values of best polynomial approximations are estimated from above via both the moduli of continuity of mth order and K-functionals of rth derivatives. For function classes defined by these characteristics, the exact values of various widths are calculated in the space L 2,ρ (ℝ). Also, for the classes \(W_{2,\rho }^r (\mathbb{K}_m ,\Psi )\), where r = 2, 3, h3, the exact values of the best polynomial approximations of the intermediate derivatives f (ν), ν = 1,..., r − 1, are obtained in L 2,ρ (ℝ).
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Original Russian Text © S. B. Vakarchuk, 2014, published in Matematicheskie Zametki, 2014, Vol. 95, No. 5, pp. 666–684.
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Vakarchuk, S.B. Mean approximation of functions on the real axis by algebraic polynomials with Chebyshev-Hermite weight and widths of function classes. Math Notes 95, 599–614 (2014). https://doi.org/10.1134/S0001434614050046
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DOI: https://doi.org/10.1134/S0001434614050046