We develop the theory of approximations in functional semilinear metric spaces that allows us to consider the classes of multi- and fuzzy-valued functions, as well as the classes of functions with values in Banach spaces, including the classes of random processes. For integral operators on the classes of functions with values in semilinear metric spaces, we obtain estimates of their deviations and discuss possible applications of these estimates to the investigation of the problems of approximation by generalized trigonometric polynomials, optimization of approximate integration formulas, and reconstruction of functions according to incomplete information.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 5, pp. 599–609, May, 2022. Ukrainian DOI: https://doi.org/10.37863/umzh.v74i5.7172.
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Babenko, V.F., Babenko, V.V., Kovalenko, O.V. et al. Estimates for the Deviations of Integral Operators in Semilinear Metric Spaces and Their Applications. Ukr Math J 74, 685–697 (2022). https://doi.org/10.1007/s11253-022-02094-2
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DOI: https://doi.org/10.1007/s11253-022-02094-2