We establish asymptotically unimprovable interpolation analogs of Lebesgue-type inequalities on the sets \( C_{\beta}^{\psi }{L_p} \) of (ψ, β)-differentiable functions generated by sequences ψ(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 \( C_{{\beta, p}}^{\psi } \), 1 ≤ p ≤ ∞.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 5, pp. 698–712, May, 2012.
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Serdyuk, A.S. Approximation by interpolation trigonometric polynomials on classes of periodic analytic functions. Ukr Math J 64, 797–815 (2012). https://doi.org/10.1007/s11253-012-0679-0
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DOI: https://doi.org/10.1007/s11253-012-0679-0