Approximation of (ψ, β)-Differentiable Functions Defined on the Real Axis by Abel-Poisson Operators

Approximation of Functions of the Classes CβψHα by Linear Methods Summation of Their Fourier Series

“…Similarly, as when proving relation (20) for a > 1 δ , we can show that equality (20) also holds for the case 1 2δ < a ≤ 1 δ . Equality ( 13) is obtained on the basis of relation (19) using condition (12), the definition of the function ξ(A, B), and formula (20). Theorem 3 is proved.…”

“…in[9][10][11][12][13][14], and at the same time, a similar problem for the classes Cψ β H α remains open.…”

Asymptotics of approximation of conjugate functions by Poisson integrals

“…The complete asymptotic decomposition of the quantity E W r ; P δ C in powers of 1 δ as δ → ∞ was obtained by Baskakov [2] for r = 1, 2, 3. Later, the Kolmogorov-Nikol'skii problem for the Poisson integral on classes of differentiable functions was solved in the works [5,[12][13][14][15]. On the other hand, approximation properties of the method of approximation by Poisson integrals on classes of conjugate functions have not been sufficiently studied.…”

Approximation of functions from the class ${\ifmmode\expandafter\hat\else\expandafter\^\fi{C}}^\psi_{\beta,\infty}$ by Poisson biharmonic operators in the uniform metric

“…In the present paper, we continue our investigation begun in [16]. In particular, we consider here the case where the function ψ(v) that defines the classĈ ψ β,∞ tends to zero as v → ∞ faster than the function 1 v 2 , which defines the order of the saturation of the linear approximation method generated by the operator B σ .…”