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Volume 59 >>> № 1 JANUARY — FEBRUARY 2023
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UDC 519.8
O.G. Khanin1, B.M. Borsuk2


1 Lesya Ukrainka Volyn National University, Lutsk, Ukraine

 aleks.hanin@ukr.net

2 Lesya Ukrainka Volyn National University, Lutsk, Ukraine

 b.borsuk@outlook.com

APPROXIMATE CHARACTERISTICS OF GENERALIZED POISSON OPERATORS
ON THE ZYGMUND CLASSES

Abstract. The paper analyzes the approximate characteristics of generalized Poisson operators on the classes of Zygmund Z α, with the aim of their further application in the theory of optimal solutions. Classes of Zygmund Z α are increasingly used in optimization methods, emphasizing the relevance of the problem. The estimation of the upper bound of the deviation of the functions of Zygmund class Z α 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 realize asymptotic approximation of the class functions Z α in the best way. That is, we have the specific implementation of the optimization problems using the methods of approximation theory.

Keywords: functions optimization properties, approximate characteristics, linear positive operators, Zygmund class.


full text

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