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International Theoretical Science Journal
Volume 62 >>> № 5 SEPTEMBER — OCTOBER 2026
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DOI 10.34229/KCA2522-9664.26.5.14
UDC 519.8

A.M. Shutovskyi
Lesya Ukrainka Volyn National University, Lutsk, Ukraine,
 sh93ar@gmail.com

K.M. Zhyhallo
Lesya Ukrainka Volyn National University, Lutsk, Ukraine,
 zhyhallo@modulsoft.eu


OPTIMIZATION CHARACTERISTICS OF ZYGMUND CLASS FUNCTIONS
FOR POSITIVE OPERATORS

Abstract. The paper is devoted to studying the optimization characteristics of Zygmund class functions in the case of controlled dynamic systems with zero initial velocity. It formulates and solves a robust optimization problem, which consists in estimating the deviation of the functions of Zygmund class Z α (0 < α ≤ 2) from positive operators as optimal solutions to boundary value problems. It is shown that the found optimization estimate is global in nature with a possibility of reproducing some previously known results.

Keywords: optimization problem, Zygmund class functions, control parameter, optimization estimate.


full text

REFERENCES

    1. Vlasenko L.A., Chikrii A.A. The method of resolving functionals for a dynamic game in a Sobolev system. Journal of Automation and Information Sciences. 2014. Vol. 46, N 7. P. 1–11. https://doi.org/10.1615/JAutomatInfScien.v46.i7.10.
    2. Baranovskaya L.V., Chikrii A.A., Chikrii Al.A. Inverse Minkowski functional in a nonstationary problem of group pursuit. Journal of Computer and Systems Sciences International. 1997. Vol. 36, N 1. P. 101–106.
    3. Chikrij A.A., Dzyubenko K.G. Bilinear markovian processes of search for moving objects. Problemy Upravleniya i Informatiki (Avtomatika). 1997. N 1. P. 92–106.
    4. Abdullayev F.G., Bushev D.M., Imashkyzy M., Kharkevych Yu.I. Isometry of the subspaces of solutions of systems of differential equations to the spaces of real functions. Ukrainian Mathematical Journal. 2020. Vol. 71, N 8. P. 1153–1172. https://doi.org/10.1007/s11253-019-01705-9.
    5. Vlasenko L.A., Rutkas A.G. On a differential game in a system described by an implicit differential-operator equation. Differential Equations. 2015. Vol. 51, N 6. P. 798–807. https://doi.org/10.1134/S0012266115060117.
    6. Shutovskyi A.M., Kharkevych Yu.I. On saturation of one linear method for summing Fourier series given by a function set. Researches in Mathematics. 2025. Vol. 33, N 1. P. 122–136. https://doi.org/10.15421/242508.
    7. Bushev D.M., Kal’chuk I.V., Kharkevych Yu.I. Approximation of isometric function spaces by entire functions of exponential type. Carpathian Mathematical Publications. 2025. Vol. 17, N 2. P. 679–692. https://doi.org/10.15330/cmp.17.2.679-692.
    8. Vlasenko L.A., Rutkas A.G. On the optimal control of systems described by implicit evolution equations. Differential Equations. 2009. Vol. 45, N 3. P. 429–438. https://doi.org/10.1134/S0012266109030124.
    9. Zhyhallo T.V., Kharkevych Yu.I. Approximation of -differentiable functions by Poisson integrals in the uniform metric. Ukrainian Mathematical Journal. 2009. Vol. 61, N 11. P. 1757–1779. https://doi.org/10.1007/s11253-010-0311-0.
    10. Kharkevych Yu.I., Kal’chuk I.V. Asymptotics of the values of approximations in the mean for classes of differentiable functions by using biharmonic Poisson integrals. Ukrainian Mathematical Journal. 2007. Vol. 59, N 8. P. 1224–1237. https://doi.org/10.1007/s11253-007-0082-4.
    11. Zhyhallo T.V., Kharkevych Yu.I. Approximating properties of biharmonic Poisson operators in the classes . Ukrainian Mathematical Journal. 2017. Vol. 69, N 5. P. 757–765. https://doi.org/10.1007/s11253-017-1393-8.
    12. Vlasenko L.A., Rutkas A.G. Optimal control of a class of random distributed Sobolev type systems with aftereffect. Journal of Automation and Information Sciences. 2013. Vol. 45, N 9. P. 65–76. https://doi.org/10.1615/JAutomatInfScien.v45.i9.60.
    13. Vlasenko L.A., Rutkas A.G. Optimal control of undamped Sobolev-type retarded systems. Mathematical Notes. 2017. Vol. 102, N 3–4. P. 297–309. https://doi.org/10.1134/S0001434617090012.
    14. Kal’chuk I., Kharkevych Yu. Approximation properties of the generalized Abel-Poisson integrals on the Weyl-Nagy classes. Axioms. 2022. Vol. 11, N 4. P. 161. https://doi.org/10.3390/axioms11040161.
    15. Zhyhallo T.V., Kharkevych Yu.I. Approximation of functions from the class by Poisson integrals in the uniform metric. Ukrainian Mathematical Journal. 2009. Vol. 61, N 12. P. 1893–1914. https://doi.org/10.1007/s11253-010-0321-y.
    16. Stepanets A.I., Serdyuk A.S., Shidlich A.L. On relationship between classes of -differentiable functions and Gevrey classes. Ukrainian Mathematical Journal. 2009. Vol. 61, N 1. P. 171–177. https://doi.org/10.1007/s11253-009-0189-x.
    17. Kal’chuk I.V., Kharkevych Yu.I. Approximating properties of biharmonic Poisson integrals in the classes . Ukrainian Mathematical Journal. 2017. Vol. 68, N 11. P. 1727–1740. https://doi.org/10.1007/s11253-017-1323-9.
    18. Shutovskyi A.M. Some representations of triharmonic functions. Cybernetics and Systems Analysis. 2024. Vol. 60, N 6. P. 991–1000. https://doi.org/10.1007/s10559-024-00735-x.
    19. Kharkevych Yu.I., Stepaniuk T.A. Approximate properties of Abel–Poisson integrals on classes of differentiable functions defined by moduli of continuity. Carpathian Mathematical Publications. 2023. Vol. 15, N 1. P. 286–294. https://doi.org/10.15330/cmp.15.1.286-294.
    20. Shutovskyi A.M., Pryt V.V. Optimization characteristics of the operator with delta-like kernel for quasi-smooth functions. Cybernetics and Systems Analysis. 2024. Vol. 60, N 5. P. 792–798. https://doi.org/10.1007/s10559-024-00716-0.
    21. Kharkevych Yu.I., Shutovskyi A.M. Approximation of functions from Hlder class by biharmonic Poisson integrals. Carpathian Mathematical Publications. 2024. Vol. 16, N 2. P. 631–637. https://doi.org/10.15330/cmp.16.2.631-637.
    22. Zhyhallo K.M., Kharkevych Yu.I. On some approximate properties of biharmonic Poisson integrals in the integral metric. Carpathian Mathematical Publications. 2024. Vol. 16, N 1. P. 303–308. https://doi.org/10.15330/cmp.16.1.303-308.
    23. Shutovskyi A., Kharkevych Yu. Structural connection between solutions to biharmonic equation and Laplace equation. Studies in Systems, Decision and Control. 2026. Vol. 609. P. 185–203. https://doi.org/10.1007/978-3-031-97529-5_12.
    24. Vlasenko L.A., Rutkas A.G., Chikrii A.O. Functional-differential games with nonatomic difference operator. Ukrainian Mathematical Journal. 2022. Vol. 74, N 2. P. 186–202. https://doi.org/10.1007/s11253-022-02057-7.
    25. Chikrii A.A., Eidelman S.D. Game problems for fractional quasilinear systems. Computers and Mathematics with Applications. 2002. Vol. 44, N 7. P. 835–851. https://doi.org/10.1016/S0898-1221(02)00197-9.
    26. Vlasenko L.A., Samoilenko A.M. Optimal control with impulsive component for systems described by implicit parabolic operator differential equations. Ukrainian Mathematical Journal. 2009. Vol. 61, N 8. P. 1250–1263. https://doi.org/10.1007/s11253-010-0274-1.
    27. Vlasenko L.A., Rutkas A.G., Semenets V.V., Chikrii A.A. On the optimal impulse control in descriptor systems. Journal of Automation and Information Sciences. 2019. Vol. 51, N 5. P. 1–15. https://doi.org/10.1615/JAutomatInfScien.v51.i5.10.



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