Counterexamples in best approximation

Poreda, S. J.

doi:10.1090/S0002-9939-1976-0402362-4

Counterexamples in best approximation
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by S. J. Poreda PDF

Proc. Amer. Math. Soc. 56 (1976), 167-171 Request permission

Abstract:

Several counterexamples for approximation to continuous functions by polynomials are given. One example shows that the points of maximum deviation of a continuous real valued function on an interval from its polynomial of degree $n$ of best uniform approximation can lie on any monotone sequence contained in that interval for infinitely many $n$.

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