The article is dedicated to the 100th anniversary of the birth of the outstanding Ukrainian mathematician by Corresponding Member of the National Academy of Sciences of Ukraine V.K. Dzyadyk. He obtained significant results in the theory of approximation of periodic functions. He belongs to the creation of a theory of constructive description of important classes of functions of a complex variable, the construction of approximation methods for solving differential and integral equations. The mathematical talent and organizational abilities of V.K. Dzyadyk contributed to the creation of a well-known school on the theory of approximation of functions. Among his students are such famous mathematicians as professors A. I. Stepanets, I. A. Shevchuk, V. M. Konovalov, Yu I. Melnyk, V. I. Bily and others. The article highlights two important tasks, the solution of which brought world-wide fame to the scientist. These are the Favard problem of the best approximation of functions with classes $W^r$ with fractional $r$ and the Kolmogorov - Nikolsky problem about the exact upper bound of the deviations of linear methods for summing Fourier series on some classes $W^r H_{\omega}$.

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