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Information × Registration Number 0216U002386, 0114U000193 , R & D reports Title Inequalities for derivatives and extremal problems of approximation in different normed spaces popup.stage_title Head Parfinovych Nataliia Viktorivna, Registration Date 29-02-2016 Organization Dniepropetrovsk national university popup.description2 Research object is inequalities for function derivatives and antiderivatives, methods of adaptive approximation of multivariate functions, perfect splines, linear methods of approximation of classes of functions with a given majorant for the modulus of continuity. The work purpose is to obtain new exact inequalities for derivatives of univariate functions in various metrics, and new exact inequalities for the Riesz fractional derivatives of multivariate functions, establish new sharp estimates on the approximation error of Hilbert space elements by an arbitrary linear method of approximation, prove existence and obtain extremal properties of perfect periodic splines, finding the best linear methods of approximation of classes of functions with a given majorant for the modulus of continuity. Research approaches include modern methods of Functions Theory, Approximation Theory, Mathematical and Functional Analysis, in particular, methods of functions and their rearrangements comparison. We proved new exact inequalities for derivatives of functions defined on real line in various metrics; obtained new exact inequalities for the norms of intermediate Riesz fractional derivatives of multivariate functions; obtained new asymptotically sharp results in extremal problems of approximation of univariate and multivariate functions by piecewise-linear and harmonic splines, linear combinations of ridge functions. We found the best linear positive minihedral method of approximation of functions with a given majorant for their modulus of continuity; established existence and some extremal properties of periodic perfect spline interpolating a given function in average; obtain new sharp estimates on the error of approximation of Hilbert space elements by an arbitrary linear method acting into the subspace of integral vectors of exponential type. These results are important because they form the basis for solving important extremal problems of analysis and approximation theory. Our results can be used in extremal problems of analysis and approximation theory, numerical mathematics, theory of ill-posed problems. Product Description popup.authors Вірьовка Тетяна Сергіївна Коваленко Олег Вікторович Конарєва Світлана Вікторівна Костюк Ольга Дмитрівна Кофанов Володимир Олександрович Лескевич Тетяна Юріївна Престинська Софія Василівна Скороходов Дмитро Сергійович Чурілова Марія Сергіївна Шевцова Світлана Євгеніївна popup.nrat_date 2020-04-02 Close