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Approximate Characteristics of Generalized Poisson Operators on Zygmund Classes

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Cybernetics and Systems Analysis Aims and scope

Abstract

The authors analyze approximate characteristics of generalized Poisson operators on Zygmund classes Zα, with the aim of their further application in the theory of optimal decisions. Nowadays, Zygmund classes Zα are increasingly used in optimization methods, which makes the problem important. An estimate of the upper bound of the deviation of functions of the Zygmund class Zα from their generalized Poisson operators in the uniform metric is obtained. Generalized Poisson operators as solutions of the corresponding elliptic partial differential equations are positive linear operators and, therefore, they implement asymptotic approximation of functions of the class Zα in the best way. That is, we get a specific implementation of the optimization problems using the methods of approximation theory.

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  1. Lesya Ukrainka Volyn National University, Lutsk, Ukraine

    O. G. Khanin & B. M. Borsuk

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  1. O. G. Khanin
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Translated from Kibernetyka ta Systemnyi Analiz, No. 1, January–February, 2023, pp. 180–190.

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Khanin, O.G., Borsuk, B.M. Approximate Characteristics of Generalized Poisson Operators on Zygmund Classes. Cybern Syst Anal 59, 156–164 (2023). https://doi.org/10.1007/s10559-023-00550-w

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