On some extremal problems of approximation theory in the complex plane - Vakarchuk, S. B. (Ukrains’kyi Matematychnyi Zhurnal, 2004)
In the Hardy Banach spaces H q , Bergman Banach spaces H′q, and Banach spaces ℬ (p, q, λ), we determine the exact values of the Kolmogorov, Bernstein, Gel’fand, linear, and trigonometric n-widths of classes of functions analytic in the disk |z| < 1 and such that the averaged moduli of continuity of their r-derivatives are majorized by a certain function. For these classes, we also consider the problems of optimal recovery and coding of functions.