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Information × Registration Number 0220U100892, 0117U001208 , R & D reports Title Extremal problems in theory of approximation of real variable functions and Kolmogorov type inequalities popup.stage_title Head Motornyi Vitalii P., Registration Date 29-01-2020 Organization Oles Honchar Dnipro National University popup.description2 The object of the research: problems of Approximation Theory, algorithms of recovery of the mathematical objects given incomplete data, problems of Numeric Analysis, Mathematical Economics and extremal problems of Analysis. The goal of the research: invention of the new methods to estimate the approximation of the functions by various approximation tools; development of new and improvement of the existing methods to solve extremal problems of Approximation Theory; solution of the problems of optimal recovery for various mathematical objects given incomplete or inaccurate information; The methods of the research: modern methods of the Theory of Functions, Approximation Theory, Optimal Algorithms Theory, Mathematical and Functional Analysis. Sharp values of the best non-symmetrical approximation in the mean of the classes of convolutions of rearrangement-invariant sets with CVD-kernels by the spaces of generalized polynomial splines with uniform knots were found. The best approximation of the functional on the class by linear bounded functionals for arbitrary normal operator were obtained. New methods for estimation of the optimal error of recovery were developed and the solutions for a series of problems of optimal recovery of operators given inexact data were obtained. New sharp inequalities of Kolmogorov type and Ostrowski type as well as sharp Remez type inequalities in different metrics were proved. The Bojanov-Naidenov extremal problem for the functions defined on the line was solved. The results are implemented into the educational process, in particular into basic specialized courses for the B. S., M. S. and PhD students of ‘Mathematics’ specialty. The areas of applications include extremal problems of Analysis, Approximation Theory, Numeric Analysis, Ill-stated problems Theory, PDE. Product Description popup.authors Kovalenko Oleksandr V. Kofanov Volodymyr O. Parfinovych Nataliia V. popup.nrat_date 2020-04-02 Close