2018
Том 70
№ 9

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

Abstract

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

English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 7, pp 1126-1138.

Citation Example: Chaichenko S. O., Rukasov V. I. Approximation by de la Vallée-Poussin operators on the classes of functions locally summable on the real axis // Ukr. Mat. Zh. - 2010. - 62, № 7. - pp. 968–978.

Full text