On the boundedness in $C_0(\Omega_\delta)$ of the de la Vall\'ee Poussin means for the Fourier--Meixner sums

Abstract

Approximation properties of the de la Vall\'ee Poussin means $V_{n+m,N}^\alpha(f,x)$ of Fourier--Meixner sums are studied.
In particular, for $an\le m\le bn$ and $n+m\le \lambda N$ the existence of a constant $c(a,b,\alpha,\lambda)$ is established such that $\|V^\alpha_{n+m,N}(f)\|\le c(a,b,\alpha,\lambda)\|f\|$, where $\|f\|$ is the norm of the function $f$ in the space $C_0(\Omega_\delta)$.