On the Best Approximation of Functions Analytic in the Disk in the Weighted Bergman Space \({{\mathcal{B}}_{{2,\mu }}}\)

Sharp inequalities between the best approximations of functions analytic in the unit disk are obtained using algebraic polynomials and the moduli of continuity of higher-order derivatives in the Bergman space \({{\mathcal{B}}_{{2,\mu }}}\) Based on these inequalities, the exact values of some known \(n\) -widths of classes of functions analytic in the unit disk are calculated.