Estimates for the Deviations of Integral Operators in Semilinear Metric Spaces and Their Applications

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 class...

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Bibliographic Details
Published inUkrainian mathematical journal Vol. 74; no. 5; pp. 685 - 697
Main Authors Babenko, V. F., Babenko, V. V., Kovalenko, O. V., Parfinovych, N. V.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.10.2022
Springer
Springer Nature B.V
Subjects
Algebra
Analysis
Applications of Mathematics
Approximation
Banach spaces
Deviation
Estimates
Geometry
Mathematical analysis
Mathematics
Mathematics and Statistics
Metric space
Operators (mathematics)
Optimization
Polynomials
Random processes
Statistics
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Summary: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.
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-022-02094-2