Abstract:

Approximation properties of the de la Vallée 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 $∥V_{n+m,N}^{\alpha} (f)∥ \le c(a, b, \alpha, \lambda) ∥f∥$, where $∥f∥$ is the uniform norm of the function f on the grid $\Omega \delta$.