On Best Simultaneous Approximation of Analytic Functions in the Weighted Bergman Space

In the Bergman space $$B_{q,\gamma}$$ $$(1\leq q<\infty$$ , $$\gamma:=\gamma(|z|)> 0)$$ , we find sharp inequalities between the best simultaneous approximation of a function and the averaged moduli of smoothness $$\omega_2(f^{(r)},t)_{H_{q,R}}$$ of the angular boundary values of the $$r$$ th derivatives. These inequalities are applied to the problem of evaluation of the supremum of best simultaneous approximations of some classes of functions defined in terms of moduli of smoothness and lying in the Bergman space $$B_{q,\gamma}$$ .