Approximation of Analytic Periodic Functions by de la Vallée-Poussin Sums

We investigate the approximation properties of the de la Vallée-Poussin sums on the classes . We obtain asymptotic equalities that, in certain cases, guarantee the solvability of the Kolmogorov–Nikol'skii problem for the de la Vallée-Poussin sums on the classes .     

Approximation of the Classes $$C^{{\bar \psi }} H_{\omega }$$ by de la Vallée-Poussin Sums

We investigate the problem of the approximation of the classes introduced by Stepanets in 1996 by the de la Valée-Poussin sums. We obtain asymptotic equalities that give a solution of the Kolmogorov–Nikol'skii problem for the de la Valée-Poussin sums on the classes in several important cases.     

Approximation of Bounded Holomorphic and Harmonic Functions by Fejér Means

Ukrainian Mathematical Journal - We compute the exact values of the least upper bounds on the classes of bounded holomorphic and harmonic functions in a unit disk for the remainders in a...     

Approximative Properties of Diagonal Operators in Orlicz Spaces

We obtain the exact values of some important approximative quantities (such as the best approximation, the basis width, Kolmogorov's width, and the best n-term approximation) of certain sets of images of the diagonal operators in the Orlicz sequence spaces l _M .     

Approximation by de la Vallée-Poussin operators on the classes of functions locally summable on the real axis

For the least upper bounds of deviations of the de la Vallée-Poussin operators on the classes [^(L)]_b^y \hat{L}_\beta^\psi of rapidly vanishing functions ψ in the metric of the spaces [^(L)]_p {\hat{L}_p} , 1 ≤ p ≤ ∞, we establish upper estimates that are exact on some subsets of functions from [^(L)]_p {\hat{L}_p} .     

Approximation of $$\overline \psi$$ -Integrals of Periodic Functions by de la Vallée-Poussin Sums (Low Smoothness)

We investigate the asymptotic behavior of the upper bounds of deviations of linear means of Fourier series from the classes . In particular, we obtain asymptotic equalities that give a solution of the Kolmogorov–Nikol'skii problem for the de la Vallée-Poussin sums on the classes .     

Approximation of classes of analytic functions by a linear method of special form

We establish asymptotic equalities for the least upper bounds of deviations of trigonometric polynomials generated by a linear approximation method of a special form on classes of convolutions of analytic functions in the uniform and integral metrics.