References

  1. Abdullayev F.G., Kharkevych Y.I. Approximation of the classes \(C^{\psi}_{\beta}H^{\alpha}\) by biharmonic Poisson integrals. Ukrainian Math. J. 2020, 72 (1), 21–38 . doi:10.1007/s11253-020-01761-6
  2. Baskakov V. A. Asymptotic estimates for approximation of conjugate functions by conjugate Abel-Poisson integrals. Appl. Funct. Analysis to Approx. Theory 1975, 5, 14–20 (in Russian).
  3. Bausov L.I. Linear methods of summing Fourier series with prescribed rectangular matrices. I. Izv. Vyssh. Uchebn. Zaved. Mat. 1965, 3 (46), 15-31. (in Russian)
  4. Kal’chuk I., Kharkevych Y. Approximation Properties of the Generalized Abel-Poisson Integrals on the Weyl-Nagy Classes. Axioms 2022, 11 (4), 161–173. doi:10.3390/axioms11040161
  5. Kal’chuk I.V., Kharkevych Yu.I. Complete asymptotics of the approximation of function from the Sobolev classes by the Poisson integrals. Acta Comment. Univ. Tartu. Math. 2018, 22 (1), 23–36. doi:10.12697/ACUTM.2018.22.03
  6. Kal’chuk I.V., Kharkevych Yu.I., Pozharska K.V. Asymptotics of Approximation of Functions by Conjugate Poisson Integrals. Carpathian Math. Publ. 2020, 12 (1), 138–147. doi:10.15330/cmp.12.1.138-147
  7. Kharkevych Yu.I. Asymptotic expansions of upper bounds of deviations of functions of class \(W^r\) from their generalized Poisson integrals. J. Automation Information Sci. 2018, 50 (8), 38–49. doi:10.1615/JAutomatInfScien.v50.i8.40
  8. Kharkevych Yu.I., Pozharska K. V. Asymptotics of approximation of conjugate functions by Poisson integrals. Acta Comment. Univ. Tartu. Math. 2018, 22 (2), 235–243. doi:10.12697/ACUTM.2018.22.19
  9. Nikolsky S.M. Approximations of periodic functions by trigonometrical polynomials. Izv. Akad. Nauk SSSR Ser. Mat. 1946, 10 (3), 207–256 (in Russian).
  10. Stepanets A.I. Methods of Approximation Theory. Part 1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev, 2002. (in Russian)
  11. Timan A. F. Sharp estimate for a remainder in the approximation of periodic differentiable functions by Poisson integrals. Dokl. Akad. Nauk SSSR 1950, 74 (1), 17–20 (in Russian).
  12. Zhyhallo K. M., Kharkevych Yu. I. Complete asymptotics of the deviation of a class of differentiable functions from the set of their harmonic Poisson integrals. Ukrainian Math. J. 2002, 54 (1), 51–63. doi:10.1023/A:1019789402502
  13. Zhyhallo T.V., Kharkevych Yu.I. Approximation of \((\psi,\beta)\)-differentiable functions by Poisson integrals in the uniform metric. Ukrainian Math. J. 2009, 61 (11), 1757–1779. doi:10.1007/s11253-010-0311-0
  14. Zhyhallo T.V., Kharkevych Yu.I. Approximation of functions from the class \(C^{\psi}_{\beta,\infty}\) by Poisson integrals in the uniform metric. Ukrainian Math. J. 2009, 61 (12), 1893–1914. doi:10.1007/s11253-010-0321-y