References

  1. Abdullayev F.G., Bushev D.M., Imashkyzy M., KharkevychYu.I. Isometry of the Subspaces of Solutions of Systems of Differential Equations to the Spaces of Real Functions. Ukrainian Math. J. 2020, 71 (8), 1153–1172. doi:10.1007/s11253-019-01705-9 (translation of Ukrain. Mat. Zh. 2019, 71 (8), 1011–1027)
  2. Akhiezer N.I. Lectures on Approximation Theory. Dover Publications, New York, 1992.
  3. Babenko V., Babenko V., Kovalenko O., Parfinovych N. Nagy type inequalities in metric measure spaces and some applications. Carpathian Math. Publ. 2023, 15 (2), 563–575. doi:10.15330/cmp.15.2.563-575
  4. Babenko V.F., Babenko V.V. Kovalenko O.V., Parfinovych N.V. On Landau-Kolmogorov Type Inequalities for Charges and Their Applications. Res. Math. 2023, 31 (1), 3–16. doi:10.15421/242301
  5. Babenko V.F., Babenko Yu.V., Parfinovych N.V. Optimal Recovery of Mappings Based on Linear Information With the Help of \(T\)-Splines in Banach Spaces. Res. Math. 2024, 32 (3), 6–11. doi:10.15421/242429
  6. Babenko V., Kolesnyk V., Kovalenko O., Parfinovych N. Kolmogorov-type inequalities in semilinear metric spaces. Carpathian Math. Publ. 2025, 17 (2), 579–590. doi:10.15330/cmp.17.2.579-590
  7. Bary N.K. A Treatise on Trigonometric Series. Volume I. Pergamon Press, New York, 1964.
  8. Bary N.K. A Treatise on Trigonometric Series. Volume II. Pergamon Press, New York, 1964.
  9. Bushev D., Abdullayev F., Kal’chuk I., Imashkyzy M. The use of the isometry of function spaces with different numbers of variables in the theory of approximation of functions. Carpathian Math. Publ. 2021, 13 (3), 805–817. doi:10.15330/cmp.13.3.805-817
  10. Bushev D.M. Isometry of Functional Spaces With Different Number of Variables. Ukrainian Math. J. 1998, 50 (8), 1170–1191. doi:10.1007/BF02513090 (translation of Ukrain. Mat. Zh. 1998, 50 (8), 1027–1045)
  11. Bushev D.M., Kharkevych Yu.I. Conditions of Convergence Almost Everywhere for the Convolution of a Function with Delta-Shaped Kernel to this Function. Ukrainian Math. J. 2016, 67 (11), 1643–1661. doi:10.1007/s11253-016-1180-y (translation of Ukrain. Mat. Zh. 2015, 67 (11), 1461–1476)
  12. Bushev D.M., Kharkevych Yu.I. Finding Solution Subspaces of the Laplace and Heat Equations Isometric to Spaces of Real Functions and Some of Their Applications. Math. Notes 2018, 103 (5–6), 869–880. doi:10.1134/S0001434618050231
  13. Bushev D.N. Isometry of the Functional Spaces with Different Number of Variables and Some its Applications in the Theory of Approximation of Functions. J. Autom. Inf. Sci. 2019, 51 (1), 70–77. doi:10.1615/JAutomatInfScien.v51.i1.70
  14. Chaichenko S.O., Shidlich A.L. Approximation of Functions by Linear Methods in Weighted Orlicz Type Spaces with Variable Exponent. Res. Math. 2024, 32 (2), 70–87. doi:10.15421/242420
  15. Dmytryshyn M. Besov-Lorentz-type Spaces and Best Approximations by Exponential Type Vectors. Int. J. Math. Anal. 2015, 9 (16), 779–786. doi:10.12988/ijma.2015.5233
  16. Dmytryshyn M. Tensor Products of Exponential Type Vectors of Unbounded Operators. Int. J. Math. Anal. 2014, 8 (11), 529–538. doi:10.12988/ijma.2014.4233
  17. Douglas S., Grafakos L. Remarks on Almost Everywhere Convergence and Approximate Identities. Acta Math. Sin. (Engl. Ser.) 2025, 41 (1), 255–272. doi:10.1007/s10114-025-3557-z
  18. Kharkevych Y., Stepaniuk T. 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
  19. Krasniqi X.Z. On the efficiency of certain operators of Abel-Poisson type in seminormed approximations. J. Anal. 2025. doi:10.1007/s41478-025-00991-w
  20. Krasniqi X.Z. The degree of approximation for functions in the generalized Hölder class via the biharmonic poisson integrals. J. Math. Sci. 2025. doi:10.1007/s10958-025-07861-7
  21. Natanson I.P. Theory of Functions of a Real Variable. Volume I. Ungar, New York, 1961.
  22. Natanson I.P. Theory of Functions of a Real Variable. Volume II. Ungar, New York, 1960.
  23. Nikol’skii S.M. Approximation of Functions of Several Variables and Imbedding Theorems. Nauka, Moscow, 1969. (in Russian)
  24. Timan A.F. Approximation Theory for Real-variable Functions. Pergamon Press, New York, 1963.
  25. Vakarchuk S.B. Best Mean-square Approximations by Entire Functions of Exponential Type and Mean \(\nu\)-widths of Classes of Functions on the Line. Math. Notes 2014, 96 (5–6), 878–896. doi:10.1134/S000143461411025X
  26. Zhyhallo K., Kharkevych Y. On some approximate properties of biharmonic Poisson integrals in the integral metric. Carpathian Math. Publ. 2024, 16 (1), 303–308. doi:10.15330/cmp.16.1.303-308