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Journal of Automation and Information Sciences
SJR: 0.238 SNIP: 0.464 CiteScore™: 0.27

ISSN Imprimir: 1064-2315
ISSN En Línea: 2163-9337

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Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v50.i8.70
pages 77-86

Approximative Properties of the Threeharmonic Poisson Integrals on the Hölder Classes

Ulyana Z. Hrabova
Lesya Ukrainka Eastern European National University, Lutsk

SINOPSIS

A solution of the Kolmogorov–Nikolsky problem for the threeharmonic Poisson integrals on the Hölder classes Hα for ∀α∈(0,1) in uniform metric is found. New task formulations of the approximation problem, as an auxiliary problem of decision making, allow one to obtain more adequate knowledge about the development of the situation, for the description of which this mathematical model was used. The proposed approach will allow building real models of the functioning of various systems (economic, ecological, social) in the conditions of limited and incomplete information, and consequently, make effective decisions based on available statistical information.

REFERENCIAS

  1. Stepanets A.I., Methods of approximation theory, In 2 parts, Part 1 [in Russian], Institut matematiki NAN Ukrainy, Kiev, 2002.

  2. Timan M.F., Approximation and properties of periodic functions [in Russian], Naukova dumka, Kiev, 2009.

  3. Kazakova A.O., Terentiev A.G., Numerical solution of boundary value problems for a polyharmonic equation, Zhurnal vychislitelnoy matematiki i matematicheskoy fiziki, 2012, 52, No. 11, 2050–2059.

  4. Chikrii A.A., On an analytic method in dynamical games of approach, Trudy Mat. Inst. Steklova, 2010, 271, 76–92.

  5. Chikrii A.A., Eidelman S.D., Generalized Mittag-Leffler matrix functions in game problems for fractional evolution equations, Kibernetika i sistemnyi analiz, 2000, No. 3, 3–32.

  6. Kharkevych Yu.I, Stepanyuk Т.A., Approximation properties of Poisson integrals for the classes <i>C</i><sub>&beta;</sub><sup>&psi;</sup><i>H</i><sup>&alpha;</sup>, Mathematical Notes, 2014, 96, No. 5, 1008–1019.

  7. Kalchuk I.V., Kharkevych Yu.I, Approximating properties of biharmonic Poisson integrals in the classes <i>W</i><sub>&beta;</sub><sup>r</sup><i>H</i><sup>&alpha;</sup>, Ukrainian Math. J., 2017, 68, No. 11, 1727–1740.

  8. Natanson I.P., On the order of approximation of a continuous &pi;-periodic function with the help of its Poisson integral, Doklady AN SSSR, 1950 , 72, No. 1, 11–14.

  9. Kharkevych Yu.I., Zhyhallo Т.V., Approximation of functions defined on the real axis by operators generated by &lambda;-methods of summation of their Fourier integrals, Ukrainian Math. J., 2004, 56, No. 9, 1509–1525.

  10. Kharkevych Yu.I., Zhyhallo T.V., Approximation of (&psi;&beta;)-differentiable functions defined on the real axis by Abel–Poisson operators, Ibid., 2005, 57, No. 8, 1297–1315.

  11. Zhyhallo T.V., Kharkevych Yu.I., Approximation of (&psi;&beta;) -differentiable functions by Poisson integrals in the uniform metric, Ibid., 2009, 61, No. 11, 1757–1779.

  12. Zhyhallo Т.V., Kharkevych Yu.I., Approximation of functions from the class <i>C</i><sub>&beta;&#8734;</sub><sup>&psi;</sup> by Poisson integrals in the uniform metric, Ibid., 2009, 61, No. 12, 1893–1914.

  13. Hembarska S.B., Zhyhallo K.M., Approximative properties of biharmonic Poisson integrals on Holder classes, Ibid., 2017, 69, No. 7, 1075–1084.

  14. Zhyhallo K.M., Kharkevych Yu.I., Approximation of (&psi;&beta;)-differentiable functions of low smoothness by biharmonic Poisson integrals, Ibid., 2012, 63, No. 12, 1820–1844.

  15. 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, Ibid., 2007, 59, No. 8, 1224–1237.

  16. Kharkevych Yu.I., Zhyhallo Т.V., Approximation of function from class <i>C</i><sub>&beta;&#8734;</sub><sup>&psi;</sup> by Poisson biharmonic operators in the uniform metric, Ibid., 2008, 60, No. 5, 769–798.

  17. Zhyhallo T.V., Kharkevych Yu.I., Approximating properties of biharmonic Poisson operators in the clasess <i>L</i><sub>&beta;,1</sub><sup>&psi;</sup>, Ibid., 2017, 69, No. 5, 757–765.

  18. Stark E.L., The complete asymptotic expansion for the measure of approximation of Abel–Poisson's singular integral for Lip 1, Ibid., 1973, 13, No. 1, 14–18.

  19. 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, Ibid., 2002, 54, No. 1, 51–63.

  20. Zhyhallo K.M., Kharkevych Yu.I., Approximation of conjugate differentiable functions by their Abel–Poisson integrals, Ibid., 2009, 61, No. 1, 86–98.

  21. Zhyhallo K.M., Kharkevych Yu.I., Approximation of differentiable periodic functions by their biharmonic Poisson integrals, Ibid., 2002, 54, No. 9, 1462–1470.

  22. Zhyhallo K.M., Kharkevych Yu.I., Approximation of conjugate differentiable functions by biharmonic Poisson integrals, Ibid., 2009, 61, No. 3, 399–413.

  23. Zhyhallo K.M., Kharkevych Yu.I., Approximation of functions from the classes <i>C</i><sub>&beta;&#8734;</sub><sup>&psi;</sup> by biharmonic Poisson integrals , Ibid., 2011, 63, No. 7, 1083–1107.

  24. Zhyhallo K.M., Kharkevych Yu.I. , On the approximation of functions of the Holder class by biharmonic Poisson integrals, Ibid., 2000, 52, No. 7, 1113–1117.

  25. Hrabova U.Z., Uniform approximations of functions of Lipschitz class by threeharmonic Poisson integrals, Journal of Automation and Information Sciences, 2017, 49, No. 12, 57–70.

  26. Zhyhallo K.M., Kharkevych Yu.I., On the approximation of functions of the Holder class by threeharmonic Poisson integrals, Ukrainian Math. J., 2001, 53, No. 6, 1012–1018.

  27. Kharkevych Yu.I., Kalchuk I.V., Approximation of (&psi;&beta;) -differentiable functions by Weierstrass integrals , Ibid., 2007, 59, No. 7, 1059–1087.

  28. Kalchuk I.V., Approximation of (&psi;&beta;)-differentiable functions defined on the real axis by Weierstrass operators , Ibid., 2007, 59, No. 9, 1342–1363.

  29. Bausov L.I., Linear methods for summing Fourier series with given rectangular matrices, II, Izvestiya Vuzov, 1966, 55, No. 6, 3–17.

  30. Hrabova U.Z., Kalchuk I.V., Stepanyuk Т.А., Approximation of functions from the classes <i>W</i><sub>&beta;</sub><sup>r</sup><i>H</i><sup>&alpha;</sup> by Weierstrass integrals, Ukrainian Math. J., 2017, 69, No. 4, 598–608.

  31. Gradshtein I.S., Ryzhik I.M., The tables of integrals, sums, series and products [in Russian], Fizmatgiz, Moscow, 1963.


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