Abstract
We investigate the approximation properties of the de la Vallée-Poussin sums on the classes \(C_{\beta }^q H_{\omega }\). We obtain asymptotic equalities that, in certain cases, guarantee the solvability of the Kolmogorov–Nikol'skii problem for the de la Vallée-Poussin sums on the classes \(C_{\beta }^q H_{\omega }\).
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Rukasov, V.I., Chaichenko, S.O. Approximation of Analytic Periodic Functions by de la Vallée-Poussin Sums. Ukrainian Mathematical Journal 54, 2006–2024 (2002). https://doi.org/10.1023/A:1024077332287
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DOI: https://doi.org/10.1023/A:1024077332287