Order Estimates for the Best Approximations and Approximations by Fourier Sums in the Classes of Convolutions of Periodic Functions of Low Smoothness in the Uniform Metric

• Date: 2014
• Main Authors: Serdyuk, A. S., Stepanyuk, T. A., Сердюк, А. С., Степанюк, Т. А.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2014
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2253
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We obtain the exact-order estimates for the best uniform approximations and uniform approximations by Fourier sums in the classes of convolutions of periodic functions from the unit balls of the spaces $L_p, 1 ≤ p < ∞$, with generating kernel $Ψ_{β}$ for which the absolute values of its Fouri...