Best linear methods for the approximation of functions of the Bergman class by algebraic polynomials

Abstract

On concentric circles $T_{ϱ} = {z ∈ ℂ: ∣z∣ = ϱ},\; 0 ≤ ϱ < 1$, we determine the exact values of the quantities of the best approximation of holomorphic functions of the Bergman class $A_p, 2 ≤ p ≤ ∞$, in the uniform metric by algebraic polynomials generated by linear methods of summation of Taylor series. For $1 ≤ p < 2$, we establish exact order estimates for these quantities.