Kharkevych Y.I., Khanin O.G.
Asymptotic properties of the solutions of higher-order differential equations on generalized Holder classes

Some asymptotic properties of the solutions to elliptic-type differential equations are analyzed using the methods of approximation theory. The approximation characteristics of Poisson-type operators as solutions of higher-order differential equations on generalized Hölder classes in a uniform metric are considered. In particular, the Kolmogorov–Nikolsky problem (in O. I. Stepanets’ terminology) of finding the upper bounds for the deviations of functions defined by the modulus of continuity from the Abel–Poisson and Gauss–Weierstrass operators in the space metric C is solved. The above-mentioned operators are an efficient tool for the analysis of the mathematical models that arise in solving many applied optimization problems. © 2023, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: Abel–Poisson operator, approximative characteristics, Gauss–Weierstrass operator, Hölder classes, Kolmogorov–Nikolsky problem, optimization properties of functions, Approximation theory, Differential equations, Mathematical operators, Abel–poisson operator, Approximative characteristic, Asymptotic properties, Gauss–weierstrass operator, Holder class, Kolmogorov, Kolmogorov–nikolsky problem, Optimisations, Optimization property of function, Properties of Functions, Computational complexity

Cite:
Kharkevych Y.I., Khanin O.G. (2023). Asymptotic properties of the solutions of higher-order differential equations on generalized Holder classes. Cybernetics and Systems Analysis, 59 (4), 139–146. doi: https://doi.org/10.1007/s10559-023-00598-8 http://jnas.nbuv.gov.ua/article/UJRN-0001415731 [In Ukrainian].