AZAR L. Approximation of functional classes with presence of restrictions

The thesis is devoted to a research of the task of approxi- mating of classes of periodic functions with presence of restrictions on a derivative of approximating functions (relative approximating), and also tasks about such classes, appropriate (relative) diameters. In the robot were used modern methods of the theory of functions, functional analysis and theory of approximation, in particular methods of a research of extremum problems of the theory of approximation with restrictions developed in operations N.P. Kornyshuck, V.M.Tikhomirov, А.А. Ligun, V.N. Konovalov, V.F. Babenko and others. Outcomes obtained in the robot, can find applications in further researches of extremum problems of the theory of approximating, which are carried on in Institute of mathematics Nat.Acad.of science of Ukraine, Kiev, Dnepropetrovsk, Donetsk, Odessa universities.