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Approximation of the image of the Lp ball under Hilbert-Schmidt integral operator

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Abstrakty
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In this article, an approximation of the image of the closed ball of the space Lp ( p>1 ) centered at the origin with radius r under Hilbert-Schmidt integral operator F(⋅): [formula] is considered. An error evaluation for the given approximation is obtained.
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art. no. 20220219
Opis fizyczny
Bibliogr. 14 poz.
Twórcy
  • Department of Mathematics and Science Education, Sivas Cumhuriyet University, 58140 Sivas, Turkey
Bibliografia
  • [1] C. Corduneanu, Integral Equations and Applications, Cambridge University Press, Cambridge, 1991.
  • [2] M. A. Krasnoselskii and S. G. Krein, On the principle of averaging in nonlinear mechanics, Uspehi Mat. Nauk (N.S.) 10 (1955), no. 3, 147–152.
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  • [8] A. Huseyin, On the p-integrable trajectories of the nonlinear control system described by the Urysohn-type integral equation, Open Mathematics 20 (2022), no. 1, 1101–1111, DOI: https://doi.org/10.1515/math-2022-0494.
  • [9] M. Poluektov and A. Polar, Modelling non-linear control systems using the discrete Urysohn operator, J. Franklin Inst. 357 (2020), 3865–3892, DOI: https://doi.org/10.1016/j.jfranklin.2020.02.030.
  • [10] R. Conti, Problemi di Controllo e di Controllo Ottimale, UTET, Torino, 1974.
  • [11] M. J. Gusev and I. V. Zykov, On extremal properties of the boundary points of reachable sets for control systems with integral constraints, Tr. Inst. Mat. Mekh. UrO RAN 23 (2017), no. 1, 103–115, DOI: https://doi.org/10.21538/0134-4889-2017-23-1-103-115.
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  • [14] R. L. Wheeden and A. Zygmund, Measure and Integral. An Introduction to Real Analysis, M. Dekker Inc., New York, 1977.
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Bibliografia
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