arXiv subjects
Publications and source records attributed to Yu. Kryakin.
This paper is devoted to the inequalities for mean values of functions from $T_{2n-1}^\perp$. The simple proof of the classical Jackson inequality in the case of the second modulus of continuity may be considered as the consequence of our estimates. The problems of the sharp constants in classical Stechkin's inequality are also discussed.
We find the order of Whitney's constants for oscillating functions
The classical Jackson-Stechkin inequality estimates the value of the best uniform approximation of a periodic function by trigonometric polynomials of degree $\le n-1$ in terms of its $r$-th modulus of smoothness $ω_r(f,δ)$. The main result of the paper is in establishing the correct order of Jackson--Stechkin constants.