Best approximations of periodic functions in generalized lebesgue spaces

In generalized Lebesgue spaces with variable exponent, we determine the orders of the best approximations in the classes of ( ψ ; β )-differentiable 2 π -periodic functions, deduce an analog of the well-known Bernstein inequality for the ( ψ ; β )-derivative, and apply this inequality to prove the i...

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Bibliographic Details
Published in:Ukrainian mathematical journal 2013-02, Vol.64 (9), p.1421-1439
Main Author: Chaichenko, S. O.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
Statistics
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Summary:In generalized Lebesgue spaces with variable exponent, we determine the orders of the best approximations in the classes of ( ψ ; β )-differentiable 2 π -periodic functions, deduce an analog of the well-known Bernstein inequality for the ( ψ ; β )-derivative, and apply this inequality to prove the inverse theorems of approximation theory in these classes.
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-013-0725-6