On the best approximation of certain classes of periodic functions by trigonometric polynomials

Details On the best approximation of certain classes of periodic functions by trigonometric polynomials On the best approximation of certain classes of periodic functions by trigonometric polynomials

2010-05-30

arxiv.org/abs/1005.5555v2

Azerbaijan Journal of Mathematics, Vol. 1, No. 1, 2011, 129-144

Mathematics

Classical Analysis and ODEs

Scientific paper

We obtain the estimates for the best approximation in the uniform metric of the classes of $2\pi $-periodic functions whose $(\psi ,\beta)$-derivatives have a given majorant $\omega$ of the modulus of continuity. It is shown that the estimates obtained here are asymptotically exact under some natural conditions on the parameters $\psi ,$ $\omega $ and $\beta $ defining the classes

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