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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Characterizing shape preserving $ L\sb 1$-approximation


Author: D. Zwick
Journal: Proc. Amer. Math. Soc. 103 (1988), 1139-1146
MSC: Primary 41A15; Secondary 26A51
MathSciNet review: 954996
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Abstract: With certain restrictions, a characterization of the best $ {L_1}$-approximation to a continuous function from the set of $ n$-convex functions is proved. Under these restrictions the best approximation is shown to be unique. The case $ n = 2$ (convex functions) is considered in more detail.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0954996-4
Article copyright: © Copyright 1988 American Mathematical Society