Khanin O.G., Borsuk B.M.
Approximate characteristics of generalized Poisson operators on the Zygmund classes

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. © 2023, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: approximate characteristics, optimization properties of functions, positive linear operators, Zygmund classes, Poisson equation, Approximate characteristic, Optimal decisions, Optimisations, Optimization method, Optimization property of function, Positive linear operators, Properties of Functions, Uniform metric, Upper Bound, Zygmund class, Mathematical operators

Cite:
Khanin O.G., Borsuk B.M. (2023). Approximate characteristics of generalized Poisson operators on the Zygmund classes. Cybernetics and Systems Analysis, 59 (1), 180–190. doi: https://doi.org/10.1007/s10559-023-00550-w http://jnas.nbuv.gov.ua/article/UJRN-0001380514 [In Ukrainian].