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

  • V. V. Savchuk


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.
How to Cite
Savchuk, V. V. “Best Linear Methods for the Approximation of Functions of the Bergman Class by Algebraic Polynomials”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, no. 12, Dec. 2006, pp. 1674–1685,
Research articles