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Article

On some constructions of a non-periodic modulus of smoothness related to the Riesz derivative

Eurasian Mathematical Journal. 2018. Vol. 9. No. 2. P. 11-21.

A new non-periodic modulus of smoothness related to the Riesz derivative is constructed. Its properties are studied in the spaces Lp(R) of non-periodic functions with 1 ≤ p ≤ +∞. The direct Jackson type estimate is proved. It is shown that the introduced modulus is equivalent to the K-functional related to the Riesz derivative and to the approximation error of the convolution integrals generated by the Fejer kernel.