Some Asymptotic Properties of Solutions to Triharmonic Equations (2024)

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1. 1. Batishchev DIMethods of Optimal Design1984MoscowRadio i Svyaz’[in Russian]Google Scholar
2. 2. A. A. Chikrii and S. D. Eidelman, “Game problems for fractional quasilinear systems,” Computers & Mathematics with Applications, Vol. 44, Iss. 7, 835–851 (2002). DOI: https://doi.org/10.1016/S0898-1221(02)00197-9.Google ScholarCross Ref
3. 3. Yu. V. Pilipenko and A. A. Chikrij, “The oscillation processes of conflict control,” Prikl. Matem. Mekh., Vol. 57, Iss. 3, 3–14 (1993).Google Scholar
4. 4. Kharkevych YuIOn some asymptotic properties of solutions to biharmonic equationsCybern. Syst. Analysis2022582251258445383510.1007/s10559-022-00457-yGoogle ScholarDigital Library
5. 5. Zhyhallo TVKharkevych YuIApproximation of (ψ, β) -differentiable functions by Poisson integrals in the uniform metricUkr. Math. J.2009611117571779288855710.1007/s11253-010-0311-0Google ScholarCross Ref
6. 6. Zhyhallo KMKharkevych YuIApproximation of conjugate differentiable functions by their Abel-Poisson integralsUkr. Math. J.20096118698256219310.1007/s11253-009-0196-yGoogle ScholarCross Ref
7. 7. Sobolev SLEquations of Mathematical Physics2013MoscowRipol Klassic[in Russian]Google Scholar
8. 8. U. Z. Hrabova, “Uniform approximations by the Poisson threeharmonic integrals on the Sobolev classes,” J. Autom. Inform. Sci., Vol. 51, Iss. 12, 46–55 (2019). DOI: https://doi.org/10.1615/JAutomatInfScien.v51.i12.50.Google ScholarCross Ref
9. 9. Shutovskyi AMSome applied aspects of the Dirac delta functionJ. Mathem. Sci. (United States)2023276568569410.1007/s10958-023-06790-7Google ScholarCross Ref
10. 10. Bushev DNKharkevich YuIFinding solution subspaces of the Laplace and heat equations isometric to spaces of real functions, and some of their applicationsMathem. Notes20181035–6869880380788210.1134/S0001434618050231Google ScholarCross Ref
11. 11. Zhyhallo TVKharkevych YuISome asymptotic properties of the solutions of Laplace equations in a unit diskCybern. Syst. Analysis202359344945610.1007/s10559-023-00579-xGoogle ScholarDigital Library
12. 12. Chikrii AMatychyn I“Riemann–Liouville, Caputo, and sequential fractional derivatives in differential games”, Annals of the InternSoc. of Dynamic Games201111618110.1007/978-0-8176-8089-3_4Google ScholarCross Ref
13. 13. Chikrii AABelousov AAOn linear differential games with integral constraintsProc. Steklov Inst. Mathem.2010269Suppl. 1698010.1134/S0081543810060076Google ScholarCross Ref
14. 14. Yu. Kharkevych, “Approximation theory and related applications,” Axioms, Vol. 11, Iss. 12, 736 (2022). DOI: https://doi.org/10.3390/axioms11120736.Google ScholarCross Ref
15. 15. Hrabova UTovkach ROn a boundary properties of functions from a classH p (p≥ 1)J. Mathem. Sci. (United States)2022264438939510.1007/s10958-022-06006-4Google ScholarCross Ref
16. 16. Zhyhallo TVKharkevych YuIFourier transform of the summatory Abel-Poisson functionCybern. Syst. Analysis202258695796510.1007/s10559-023-00530-0Google ScholarDigital Library
17. 17. Chikrii AAProkopovich PVSimple pursuit of one evader by a groupCybern. Syst. Analysis1992283438444119086310.1007/BF01125424Google ScholarCross Ref
18. 18. L. A. Vlasenko, A. G. Rutkas, V. sem*nets, and A. A. Chikrii, “On the optimal impulse control in descriptor systems,” J. Autom. Inform. Sci., Vol. 51, Iss. 5, 1–15 (2019). DOI: https://doi.org/10.1615/JAutomatInfScien.v51.i5.10.Google ScholarCross Ref
19. 19. I. Kal’chuk and Yu. Kharkevych, “Approximation properties of the generalized Abel–Poisson integrals on the Weyl–Nagy classes,” Axioms, Vol. 11, Iss. 4, 161 (2022). DOI: https://doi.org/10.3390/axioms11040161.Google ScholarCross Ref
20. 20. T. V. Zhyhallo and Yu. I. Kharkevych, “On approximation of functions from the class L^ψ_β,1 by the Abel–Poisson integrals in the integral metric,” Carpathian Mathem. Publ., Vol. 14, Iss. 1, 223–229 (2022). DOI: https://doi.org/10.15330/cmp.14.1.223-229.Google ScholarCross Ref
21. 21. Zhyhallo TVKharkevych YuIApproximation of functions from the class C^ψ_β,∞ by Poisson integrals in the uniform metricUkr. Math. J.2009611218931914288856710.1007/s11253-010-0321-yGoogle ScholarCross Ref
22. 22. Yu. I. Kharkevych and K. V. Pozharska, “Asymptotics of approximation of conjugate functions by Poisson integrals,” Acta et Commentationes Universitatis Tartuensis de Mathematica, Vol. 22, Iss. 2, 235–243 (2018). DOI: https://doi.org/10.12697/ACUTM.2018.22.19.Google ScholarCross Ref
23. 23. U. Z. Hrabova, “Approximation of conjugate periodic functions by their threeharmonic Poisson integrals,” J. Autom. Inform. Sci., Vol. 52, Iss. 10, 42–51 (2020). DOI: https://doi.org/10.1615/JAutomatInfScien.v52.i10.30.Google ScholarCross Ref
24. 24. U. Z. Hrabova and I. V. Kal’chuk, “Approximation of continuous functions given on the real axis by three-harmonic Poisson operators,” J. Mathem. Sci. (United States), Vol. 274, No. 3, 327–339 (2023).Google Scholar
25. 25. DOI: https://doi.org/10.1007/s10958-023-06603-x.Google ScholarCross Ref
26. 26. Kharkevych YuIExact values of the approximations of differentiable functions by Poisson-type integralsCybern. Syst. Analysis2023592274282456700210.1007/s10559-023-00561-7Google ScholarDigital Library
27. 27. U. Z. Hrabova and I. V. Kal’chuk, “Approximation of classes C ^ψ_β,∞ by three-harmonic Poisson integrals in uniform Metric (Low Smoothness),” J. Mathem. Sci. (United States), Vol. 268, No. 2, 178–191 (2022). DOI: https://doi.org/10.1007/s10958-022-06190-3.Google ScholarCross Ref
28. 28. I. V. Kal’chuk and Yu. I. Kharkevych, “Approximation of the classes W^R_β,∞ by generalized Abel–Poisson integrals,” Ukr. Math. J., Vol. 74, No. 4, 575–585 (2022). DOI: https://doi.org/10.1007/s11253-022-02084-4.Google ScholarCross Ref
29. 29. T. V. Zhyhallo and Yu. I. Kharkevych, “Approximating properties of biharmonic Poisson operators in the classes,L^ψ_β1,” Ukr. Math. J., Vol. 69, No. 5, 757–765 (2017).https://doi.org/ DOI: https://doi.org/10.1007/s11253-017-1393-8.Google ScholarCross Ref
30. 30. Zhyhallo KMKharkevych YuIApproximation of conjugate differentiable functions by biharmonic Poisson integralsUkr. Math. J.2009613399413256221610.1007/s11253-009-0217-xGoogle ScholarCross Ref
31. 31. Shutovskyi AMYe VSakhnyuk, “Taylor series of biharmonic Poisson integral for upper half-plane”J. Mathem. Sci. (United States)2022268223924610.1007/s10958-022-06195-yGoogle ScholarCross Ref
32. 32. Yu. I. Kharkevych, “Approximative properties of the generalized Poisson integrals on the classes of functions determined by a modulus of continuity,” J. Autom. Inform. Sci., Vol. 51, Iss. 4, 43–54 (2019). DOI: https://doi.org/10.1615/JAutomatInfScien.v51.i4.40.Google ScholarCross Ref
33. 33. Zhigallo KMKharkevych YuIOn the approximation of functions of the Hölder class by biharmonic Poisson integralsUkr. Math. J.20005271113111710.1023/A:1005285818550Google ScholarCross Ref
34. 34. Yu. I. Kharkevych and T. A. Stepaniuk, “Approximate properties of Abel–Poisson integrals on classes of differentiable functions defined by moduli of continuity,” Carpathian Mathem. Publ., Vol. 15, Iss. 1, 286–294 (2023). DOI: https://doi.org/10.15330/cmp.15.1.286-294.Google ScholarCross Ref
35. 35. Kharkevych YuIKhanin OGAsymptotic properties of the solutions of higher-order differential equations on generalized Hölder classesCybern. Syst. Analysis202359463363910.1007/s10559-023-00598-8Google ScholarDigital Library
36. 36. Chikrii AARappoport ISChikrii KAMultivalued mappings and their selectors in the theory of conflict-controlled processesCybern. Syst. Analysis2007435719730247939710.1007/s10559-007-0097-8Google ScholarDigital Library
37. 37. Chikrij AADzyubenko KG“Bilinear Markovian processes of search for moving objects”, Problemy Upravleniya i Informatiki (Avtomatika)No.1997192106Google Scholar
38. 38. P. V. Prokopovich and A. A. Chikrii, “A linear evasion problem for interacting groups of objects,” J. Applied Math. Mech., Vol. 58, Iss. 4, 583–591 (1994). DOI: https://doi.org/10.1016/0021-8928(94)90135-X.Google ScholarCross Ref
39. 39. Bushev DMKharkevych YuIConditions of convergence almost everywhere for the convolution of a function with delta-shaped kernel to this functionUkr. Math. J.2016671116431661351066010.1007/s11253-016-1180-yGoogle ScholarCross Ref
40. 40. D. M. Bushev, F. G. Abdullayev, I. V. Kal’chuk, and M. Imashkyzy, “The use of the isometry of function spaces with different numbers of variables in the theory of approximation of functions,” Carpathian Mathem. Publ., Vol. 13, Iss. 3, 805–817 (2021). DOI: https://doi.org/10.15330/cmp.13.3.805-817.Google ScholarCross Ref
41. 41. Zajac JKorenkov MEKharkevych YuIOn the asymptotics of some Weierstrass functionsUkr. Math. J.2015671154158340361010.1007/s11253-015-1070-8Google ScholarCross Ref
42. 42. A. S. Serdyuk and U. Z. Hrabova, “Order estimates of the uniform approximations by Zygmund sums on the classes of convolutions of periodic functions,” Carpathian Mathem. Publ., Vol. 13, Iss. 1, 68–80 (2021). DOI: https://doi.org/10.15330/cmp.13.1.68-80.Google ScholarCross Ref
43. 43. Abdullayev FGBushev DMImashkyzy MKharkevych YuIIsometry of the subspaces of solutions of systems of differential equations to the spaces of real functionsUkr. Math. J.202071811531172400322210.1007/s11253-019-01705-9Google ScholarCross Ref
44. 44. Shutovskyi AMYe VSakhnyuk, “Representation of Weierstrass integral via Poisson integrals”J. Mathem. Sci. (United States)202125919710310.1007/s10958-021-05602-0Google ScholarCross Ref

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