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Information × Registration Number 0225U003355, (0122U001461) , R & D reports Title The optimization of approximation to functions and recovery of operators, the inequalities for derivatives popup.stage_title Оптимізація наближення функцій та відновлення операторів, нерівності для похідних Head Parfinovych Nataliia V., Доктор фізико-математичних наук Registration Date 21-06-2025 Organization Oles Honchar Dnipro National University popup.description1 Developing new methods of proving the sharp inequalities for derivatives with various domains, in particular, the operator approach to getting the sharp Kolmogorov type inequalities; developing new methods of approximation to unbounded operators by linear bounded and recovery of operators using incomplete and incorrect information. popup.description2 Object of research - inequalities for derivatives of functions with different domains of definition; approximation of classes of functions and restoration of mathematical objects with incomplete information. The subject of the research is the optimal approximation of individual functions and classes of functions by various approximation devices; optimal algorithms for the recovery of functions, functionalities and operators with incomplete and inaccurate information about them; extreme properties of approximation units; exact inequalities for derivatives of functions with various domains of definition and their application to solve extreme problems of analysis and approximation theory. The goal is to create new methods for proving exact inequalities for functional derivatives with various domains, in particular, an operator approach to obtaining exact inequalities of the Kolmogorov type; to develop new methods for approximating unbounded operators by linear bounded operators and recovering operators from incomplete and inaccurate information. A number of topical problems in the theory of optimisation of approximations and recovery of operators are solved in new formulations that have arisen in the course of recent research, the interrelationships between extreme problems of the theory of approximation and exact inequalities for derivatives are investigated, and a number of such inequalities are proved. It is the solution of these problems that will determine the development of the theory of approximation optimisation and operator recovery in the coming years, and this is the relevance of the tasks of this work. Product Description popup.authors Bilichenko Roman O. Borsch Volodymyr L. Vakarchuk Mikhaylo B Kovalenko Oleh Kohut Petro І. Konareva Svitlana V Kofanov Volodymyr O. Leskevych Tetiana Yu. Parfinovych Nataliia V. Pasko Anatolii M. Siasiev Andrii V Tkachenko Maryna Ye. Traktynska Viktoriia M. popup.nrat_date 2025-06-21 Close