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Information × Registration Number 0212U007407, 0112U005707 , R & D reports Title The investigation of approximation properties of classes of periodical functions of one and many variables popup.stage_title Head Ovsii Ievgen Yuriyovych, Registration Date 25-12-2012 Organization Institute of mathematics NAS of Ukraine popup.description2 Within the limits of the research scientific work the contemporary problems of approximation theory of functions are covered. Particularly it is found the solution of the famous Kolmogorov-Nikol'skii problem on classes of periodical differentiable (in the sense of Stepanets) functions for trigonometric sums of a special type that in many cases have better approximation properties in comparison with Fourier sums, Zygmund sums, de la Vallee Poussin sums. The asymptotic equalities for the least upper bounds of approximation the classes of Poisson integrals of functions from a set defined by majorant of a type of the modulus of continuity by de la Vallee Poussin sums are obtained. For the particular classes of (psi,beta)-differentiable functions the asymptotic unimprovable estimates of deviations in the uniform metric of de la Vallee Poussin that are represented in terms of values of the best approximation of (psi,beta)-derivatives of such functions by trigonometric polynomials in the integral metrics are found. The exact order estimates of orthoprojection width of some classes of periodical functions of many variables with majorant of their mixed modulus of continuity containing the power and logarithmic multipliers are obtained. All results have a completed form and are important not only for solving the problems of the approximation theory but also for many applied mathematical problems. Product Description popup.authors Конограй Андрій Федорович Мусієнко Андрій Петрович popup.nrat_date 2020-04-02 Close