Approximation of continuous functions given on the real axis by three-harmonic Poisson operators

Abstract

Approximation properties of three-harmonic Poisson operators on the classes of $(\psi,\beta)$-differentiable functions of low smoothness given on the real axis have been studied. Asymptotic equalities have been obtained that provide in some cases a solution to the Kolmogorov--Nikol'skii problem for three-harmonic Poisson operators $P_{3,\sigma}(f;x)$ on the classes $\widehat{C}_{\beta,\infty}^{\psi}$, $\beta\in\mathbb{R}$, in the uniform metric.