Abstract
We study the rate of convergence of the Taylor series for functions from the classes A Ψ H p, p = 1, ∞, in the uniform and integral metrics.
References
S. B. Stechkin, “An estimate for the remainder of the Taylor series for certain classes of analytic functions,” Izv. Akad. Nauk SSSR, Ser. Mat., 17, No. 5, 451–472 (1953).
L. V. Taikov, “On methods of summation of Taylor series,” Usp. Mat. Nauk, 17, No. 1, 252–254 (1962).
A. I. Stepanets, Classification and Approximation of Periodic Functions [in Russian], Naukova Dumka, Kiev (1987).
A. I. Stepanets, “On the Lebesgue inequality on the classes of (Ψ, β)-differentiable functions,” Ukr. Mat. Zh., 41, No. 5, 499–510 (1989).
K. I. Babenko, “Best approximations of classes of analytic functions,” Izv. Akad. Nauk SSSR, Ser. Mat., 22, No. 5, 631–640 (1958).
L. V. Taikov, “On best linear methods of approximation of the classes B r and H r,” Usp. Mat. Nauk, 18, No. 4, 183–189 (1963).
M. Z. Dveirin, “On the approximation of functions analytic in a unit disk,” Metr. Vopr. Teor. Funkts. Otobrazh., No. 5, 41–54 (1975).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 7, pp. 1001–1003, June, 1998.
Rights and permissions
About this article
Cite this article
Savchuk, V.V. Rate of convergence of the Taylor series for some classes of analytic functions. Ukr Math J 50, 1141–1144 (1998). https://doi.org/10.1007/BF02528826
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02528826