On Simultaneous Approximation of Certain Classes of Functions in the Bergman Space B₂

The problem of finding the supremums of the best simultaneous polynomial approximations of some classes of functions analytic in the unit disk and belonging to the Bergman space \({{B}_{2}}\) is considered. The indicated function classes are defined by the averaged values of the \(m\) th-order moduli of continuity of the highest derivative bounded from above by some majorant \(\Phi \) .