Abstract
It is shown that a function inL 1 has a best approximation by convex functions, and that the net of bestL p approximations converges asp decreases to one.
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Gifford, D., Huotari, R. BestL 1 approximation by convex functions. Numer Algor 9, 107–111 (1995). https://doi.org/10.1007/BF02143929
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DOI: https://doi.org/10.1007/BF02143929