Meansquare Approximation of Function Classes, Given on the all Real Axis R by the Entire Functions of Exponential Type

Vakarchuk, Sergey B.

doi:10.18052/www.scipress.com/IJARM.6.1

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Meansquare Approximation of Function Classes, Given on the all Real Axis R by the Entire Functions of Exponential Type

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Abstract:

K-functionals K (f, t, L₂(R), L₂^β(R), which defined by the fractional derivatives of order β>0, have been considered in the space L₂(R). The relation K (f, t^β, L₂(R), L₂^β(R) ≈ ω_β(f, t) (t>0) was obtained in the sense of the weak equivalence, where ωω_β(f, t) is the module of continuity of the fractional order β for a function f є L₂(R). Exact values of the best approximation by entire functions of exponential type v∏, v є (0, ∞) have been computed for the classes of functions, given by the indicated K-functionals and majorants Ψ satisfying specific restriction. Kolmogorov, Bernsteinand linear mean v-widths were obtained for indicated classes of functions.

Info:

Periodical:

International Journal of Advanced Research in Mathematics (Volume 6)

Pages:

1-12

DOI:

https://doi.org/10.18052/www.scipress.com/IJARM.6.1

Citation:

S. B. Vakarchuk, "Meansquare Approximation of Function Classes, Given on the all Real Axis R by the Entire Functions of Exponential Type", International Journal of Advanced Research in Mathematics, Vol. 6, pp. 1-12, 2016

Online since:

September 2016

Authors:

Sergey B. Vakarchuk

Keywords:

Best Approximations, Entire Function of Exponential Type, K-Functional, Majorant, Mean v-Width

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Creative Commons Attribution 4.0 International License

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Cited By:

[1] S. Vakarchuk, "Generalized Characteristics of Smoothness and Some Extreme Problems of the Approximation Theory of Functions in the Space L2(ℝ). I", Ukrainian Mathematical Journal, 2019

DOI: https://doi.org/10.1007/s11253-019-01585-z

[2] S. Vakarchuk, "Generalized Characteristics of Smoothness and Some Extreme Problems of the Approximation Theory of Functions in the Space L2(ℝ). II", Ukrainian Mathematical Journal, 2019

DOI: https://doi.org/10.1007/s11253-019-01590-2