Estimates for deviation of integral operators in semilinear metric spaces and their applications

• Дата: 2022
• Автори: Babenko , V. F., Babenko , V. V., Kovalenko , O. V., Parfinovych , N. V., Бабенко, В. Ф., Бабенко, В. В., Коваленко, O. В., Парфінович, Н. В.
• Формат: Стаття
• Мова: Українська
• Опубліковано: Institute of Mathematics, NAS of Ukraine 2022
• Онлайн доступ: https://umj.imath.kiev.ua/index.php/umj/article/view/7172
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.5 In this paper, we develop the theory of approximations in functional semilinear metric spaces, which allows us to consider classes of multi- and fuzzy-valued functions, as well as classes of Banach space-valued functions including classes of random processes. For integral operators on classes of functions with values in semilinear metric spaces, we obtain estimates of their deviations and discuss possible applications of these estimates to studying problems of approximation by generalized trigonometric polynomials, optimization of approximate integration formulas, and recovery of functions under the conditions of incomplete information.