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.