TY - JOUR AU - A. S. Serdyuk PY - 2012/05/25 Y2 - 2024/03/29 TI - Approximation by interpolation trigonometric polynomials on classes of periodic analytic functions JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 64 IS - 5 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2609 AB - We establish asymptotically unimprovable interpolation analogs of Lebesgue-type inequalities on the sets $C^{\psi}_{\beta}L_p$ of $(\psi, \beta)$-differentiable functions generated by sequences $\psi(k)$ that satisfy the d'Alembert conditions. We find asymptotic equalities for the least upper bounds of approximations by interpolation trigonometric polynomials on the classes $C^{\psi}_{\beta, p},\;\; 1 \leq p \leq \infty$. ER -