K-Functionals and Extreme Problems of the Approximation Theory for Classes of Analytic Functions in a Circle. I

On the basis of the Hadamard composition, we consider a generalization of the K-functional in the Hardy, Bergman, and Gvaradze Banach spaces of functions analytic in a unit circle. In the solution of some extreme problems of approximation theory in the complex plane, we obtain exact results in the case where the indicated K-functional is used as a characteristic of smoothness of the functions.