Far Eastern Mathematical Journal

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On the value of the widths of some classes of functions from L_2


Langarshoev M.R.

2021, issue 1, Ń. 61-70
DOI: https://doi.org/10.47910/FEMJ202106


Abstract
In this paper we find sharp inequalities of Jackson-Stechkin type between the best approximations of periodic differentiable functions by trigonometric polynomials and generalized moduli of continuity of m-th order in the space L_2. The exact values of various n-widths of classes of functions from L_2 defined by the generalized modus of continuity of the $r$-th derivative of the function f are calculated.

Keywords:
best approximation, trigonometric polynomials, generalized modulus of continuity of higher order, n-widths

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References

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