On the best simultaneous approximation of functions in the Bergman space $B_{2}$

In the work extremal problems related to the best simultaneous polynomial approximation of analytic functions in the unit disc belonging to the Bergman space $B_{2}$ is studied. Here, a number of exact theorems and the exact values of the upper bounds of the best joint approximations of functions and its consecutive derivatives polynomials and their corresponding derivatives on some classes of complex functions belonging to the Bergman space $B_{2}$ are obtained.