Order estimation of the best approximations and of the approximations by Fourier sums of classes of (ψ,β)--diferentiable functions

الأصل · EN

There were established the exact-order estimations of the best uniform approximations byψ the trigonometrical polynoms on the Cψᵦ,ₚ classes of 2π-periodic continuous functions f, which are defined by the convolutions of the functions, which belong to the unit ball in Lₚ, 1≤ p <∞ spaces with generating fixed kernels Ψβ⊂|Lₚ', 1/p+1/p'=1, whose Fourier coeficients decreasing to zero approximately as power functions. The exact order estimations were also established in Lₚ-metrics, 1 < p ≤∞ for Lψᵦ,₁ classes of 2π-periodic functions f, which are equivalent by means of Lebesque measure to the convolutions of Ψβ⊂|Lₚ kernels with the functions that belong to the unit ball in L₁ space. We showed that in investigating cases the orders of best approximations are realized by Fourier sums.