On some extremal problems of approximation theory in the complex plane

In the Hardy Banach spaces H_q, Bergman Banach spaces H_q, and Banach spaces (p, q, ), we determine the exact values of the Kolmogorov, Bernstein, Gelfand, 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.__________Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 9, pp. 1155–1171, September, 2004.