Abstract:An approximating family is called alternating if a best Chebyshev approximation is characterized by its error curve having a certain number of alternations. The convergence properties of such families are studied. A sufficient condition for the limit of best approximation on subsets to converge uniformly to the best approximation is given: it is shown that this is often (but not always) a necessary condition. A sufficient condition for the Chebyshev operator to be continuous is given: it is shown that this is often (but not always) a necessary condition.
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- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 178 (1973), 95-109
- MSC: Primary 41A50
- DOI: https://doi.org/10.1090/S0002-9947-1973-0318736-8
- MathSciNet review: 0318736