Approximation of 2π-periodic functions by Taylor—Abel—Poisson operators in the integral metric

1Prestin, J, 2Savchuk, VV, 2Shidlich, AL
1Institute of Mathematics, University of Lübeck, Germany
2Institute of Mathematics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2017, 1:17-20
Section: Mathematics
Language: English

We obtain direct and inverse approximation theorems of 2π-periodic functions by Taylor — Abel — Poisson operators in the integral metric.

Keywords: direct approximation theorem, inverse approximation theorem, K-functional, linear approximation method
  1. Savchuk V.V. Ukr. Math. J., 2007, 59, No 9: 1397-1407.
  2. Savchuk V.V., Shidlich, A.L. Acta Sci. Math., 2014, 80, No 3-4: 477-489.
  3. Leis R. Arch. Math., 1963, 14: 120-129.
  4. Butzer P.L., Sunouchi G. Math. Ann., 1964, 155: 316-330.
  5. Rudin W. Function theory in polydiscs, New York: Benjamin, 1969.
  6. DeVore R.A., Lorentz G.G. Constructive approximation, Berlin: Springer, 1993.