ОЦІНКА ШВИДКОСТІ НАБЛИЖЕННЯ ОБРАЗАМИ ОПЕРАТОРІВ ТИПУ АБЕЛЯ–ПУАССОНА ДЕЯКИХ СПЕЦІАЛЬНИХ КЛАСІВ ФУНКЦІЙ
The properties of Abel–Poisson type operators, which have a wide range of applications in various fields of scientific research are studied. Special attention is paid to the approximation and differential properties of operators of Abel–Poisson type. In particular, an estimate was obtained for the a...
Збережено в:
| Дата: | 2025 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
V.M. Glushkov Institute of Cybernetics of NAS of Ukraine
2025
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| Теми: | |
| Онлайн доступ: | https://jais.net.ua/index.php/files/article/view/656 |
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| Назва журналу: | Problems of Control and Informatics |
Репозитарії
Problems of Control and Informatics| Резюме: | The properties of Abel–Poisson type operators, which have a wide range of applications in various fields of scientific research are studied. Special attention is paid to the approximation and differential properties of operators of Abel–Poisson type. In particular, an estimate was obtained for the approximation rate by the images of operators of Abel–Poisson type for functions having a given majorant of the type of the second modulus of continuity of the r-derivative Vall–Poussin sum of order (n, 2n) in the integral metric Lp(D). For further consideration of the differential properties of operators of Abel–Poisson type, the paper presents definitions of classes of functions that are a generalization of classes of differentiable functions of S.M. Nikolʼskii. Operators of the Abel–Poisson type are among the main ones used in real and complex analysis and mathematical physics, and their images, which are differentiable functions, are often viewed as solutions of known boundary value problems. Therefore, the result obtained in the paper can be used to study the boundary properties of operators of Abel–Poisson type and is adjacent to the similar results ofYa.S. Bugrov. In addition, it is possible to use the described properties of these operators in the theory of game dynamics problems, which is especially important nowadays, for example, in finding stationary targets that have crashed and are in practically inaccessible places when developing computer search systems and monitoring moving objects, in the analysis and modeling of group interaction between moving objects. Such tasks often arise in the maintenance of sea and air transport. |
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