Jackson–Stechkin type inequalities between the best polynomial approximations and generalized moduli of continuity in the weighted Bergman space $\mathscr{B}_{2,\gamma}$

We obtain sharp Jackson–Stechkin type inequalities for a generalized higher-order modulus of continuity and calculate the exact values of some known $n$-widths of classes of analytic functions defined by using this characteristic in the weighted Bergman space.