Abstract
The speeds of convergence of best rational approximations, best polynomial approximations, and the modulus of continuity on the unit disc are compared. We show that, in a Baire category sense, it is expected that subsequences of these approximants will converge at the same rate. Similar problems on the interval [−1, 1] are also examined. A problem raised by P. Turán ( J. Approx. Theory 29, 1980, 23-89) concerning rational approximation to non-analytically continuable ƒ on the unit circle is negated as an application.
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