On the uniform boundedness of Vallée Poussin means in the system of Meixner polynomials

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 $\|V^\alpha_{n+m,N}(f)\|\le c(a,b,\alpha,\lambda)\|f\|$, where $\|f\|$ is the uniform norm of the function $f$ on the grid $\Omega_\delta$.