Estimations of the best approximations of classes of infinitely differentiable functions in uniform and integral metrics

Abstract

We find uniform with respect to parameter $p(1\le p\le \infty )$ upper estimations of best approximations by trigonometric polynomials of classes $C_{\beta ,p}^{\psi }$ of periodic functions generated by sequences $\psi (k)$, that decrease to nought faster than any power function. Obtained estimations are exact for order and have constants that are written in explicit form and depend on function $\psi$ only. We obtain analogical estimations for best approximations of classes $L_{\beta ,1}^{\psi }$ in metrics of spaces $L_s$, $1\le s\le \infty$.

arXiv commentin Ukrainian

References in corpus (1)

• Uniform approximation of periodical functions by trigonometric sums of a special type