References
- Kaniev S. On the deviation of functions biharmonic in a disk from
their boundary values. Dokl. Akad. Nauk 1963, 153
(5), 995–998.
- Kharkevych Yu.I., Stepaniuk T.A. Approximate properties of
Abel-Poisson integrals on classes of differentiable functions defined by
moduli of continuity. Carpathian Math. Publ. 2023,
15 (1), 286–294. doi:10.15330/cmp.15.1.286-294
- Stepanets A.I. Methods of Approximation Theory. Part I. Institute of
Mathematics, Ukrainian Academy of Sciences, Kiev, 2002. (in Russian)
- Stepanets A.I. Classification and approximation of periodic
functions. Naukova Dumka, Kiev, 1987. (in Russian)
- Stepanets A.I. Uniform Approximations by Trigonometric Polynomials.
Naukova Dumka, Kiev, 1981. (in Russian)
- Pych P. On a biharmonic function in unit disc. Ann. Polon.
Math. 1975, 20 (3), 203–213.
doi:10.4064/AP-20-3-203-213
- Kaniev S. Sharp estimate for the mean deviation of functions
biharmonic in a disk from their boundary values. Dopov. Akad. Nauk
Ukr. RSR 1964, 4, 451–453.
- Amanov T.I., Falaleev L.P. Approximation of differentiable
functions by operators of the Abel-Poisson-type. Proceedings of the
5th Soviet-Czechoslovakian Meeting on Application of Methods of Theory
of Functions and Functional Analysis to Problems of Mathematical Physics
(Alma-Ata), 1979, 13–16. (in Russian)
- Falaleev L.P. Complete asymptotic expansion for an upper bound of
the deviation of functions belonging to \(\textrm{Lip}_1\) from one singular
integral. Imbedding Theorems and Their Applications (All-Union
Mathematical Symposium), Nauka, Alma-Ata, 1976, 163–167. (in
Russian)
- Kharkevych Y.I. On Some Asymptotic Properties of Solutions to
Biharmonic Equations. Cybernet. Systems Anal. 2022,
58 (2), 251–258. doi:10.1007/s10559-022-00457-y
- Kharkevych Yu.I., Kalchuk I.V. Asymptotics of the values of
approximations in the mean for classes of differentiable functions by
using biharmonic Poisson integrals. Ukrainian Math. J. 2007,
59 (8), 1224–1237. doi:10.1007/s11253-007-0082-4
(translation of Ukrain. Mat. Zh. 2007, 59 (8),
1105–1115)
- Zhyhallo K.M., Kharkevych Yu.I. Approximation of functions from
the classes \(C^{\psi}_{\beta,
\infty}\) by biharmonic Poisson integrals. Ukrainian Math.
J. 2011, 63 (7), 1083–1107.
doi:10.1007/s11253-011-0565-1 (translation of Ukrain. Mat. Zh. 2011,
63 (7), 939–959)
- Zhyhallo K.M., Kharkevych Yu.I. Approximation of \((\psi, \beta)\)-differentiable functions of
low smoothness by biharmonic poisson integrals. Ukrainian Math. J.
2012, 63 (12), 1820–1844. doi:10.1007/s11253-012-0616-2
(translation of Ukrain. Mat. Zh. 2012, 63 (12),
1602–1622)
- Korneichuk N.P. Extremal problems in approximation theory. Nauka,
Moskow, 1976. (in Russian)
- Kharkevych Yu.I., Stepanyuk T.A. Approximation properties of
Poisson integrals for the classes \(C^{\psi}_{\beta}H^{\alpha}\). Math.
Notes 2014, 96 (5–6), 1008–1019.
doi:10.1134/S0001434614110406
- Zhyhallo T., Kharkevych Y. On Approximation of functions from the
class \(L^{\psi}_{\beta, 1}\) by the
Abel–Poisson integrals in the integral metric. Carpathian Math.
Publ. 2022, 14 (1), 223–229.
doi:10.15330/cmp.14.1.223-229