We find asymptotic equalities for the exact upper bounds of approximations by Fourier sums of Weyl-Nagy classes $W^r_{\beta,p}, 1\le p\le\infty,$ for rapidly growing exponents of smoothness $r$ $(r/n\rightarrow\infty)$ in the uniform metric. We obtain similar estimates for approximations of the classes $W^r_{\beta,1}$ in metrics of the spaces $L_p, 1\le p\le\infty$.
A. S. Serdyuk and I. V. Sokolenko, Approximation by Fourier sums in classes of differentiable functions with high exponents of smoothness, Methods Funct. Anal. Topology 25
(2019), no. 4, 381-387.
BibTex
@article {MFAT1245,
AUTHOR = {A. S. Serdyuk and I. V. Sokolenko},
TITLE = {Approximation by Fourier sums in classes of differentiable functions with high exponents of smoothness},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {25},
YEAR = {2019},
NUMBER = {4},
PAGES = {381-387},
ISSN = {1029-3531},
MRNUMBER = {MR4049692},
URL = {http://mfat.imath.kiev.ua/article/?id=1245},
}