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On the Estimates of Widths of the Classes of Functions Defined by the Generalized Moduli of Continuity and Majorants in the Weighted Space L2,x(0, 1)

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Ukrainian Mathematical Journal Aims and scope

The upper and lower estimates for the Kolmogorov, linear, Bernstein, Gelfand, projective, and Fourier widths are obtained in the space L2,x(0, 1) for the classes of functions \( {W}_2^r\left({\Omega}_{m,x}^{(v)};\Psi \right), \) where r ∈ ℤ+, m ∈ ℕ, v ≥ 0, and \( {\Omega}_{m,x}^{(v)} \) and Ψ are the m th order generalized modulus of continuity and the majorant, respectively. The upper and lower estimates for the suprema of Fourier–Bessel coefficients are also established for these classes. We also present the conditions for majorants under which it is possible to find the exact values of the indicated widths and the upper bounds of the Fourier–Bessel coefficients.

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Authors and Affiliations

  1. Nobel University, Dnepr, Ukraine

    S. B. Vakarchuk

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  1. S. B. Vakarchuk
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Correspondence to S. B. Vakarchuk.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, No. 2, pp. 179–189, February, 2019.

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Vakarchuk, S.B. On the Estimates of Widths of the Classes of Functions Defined by the Generalized Moduli of Continuity and Majorants in the Weighted Space L2,x(0, 1). Ukr Math J 71, 202–214 (2019). https://doi.org/10.1007/s11253-019-01639-2

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