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Proceedings of the American Mathematical Society

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



On simultaneous Chebyshev approximation in the ``sum'' norm

Author: William H. Ling
Journal: Proc. Amer. Math. Soc. 48 (1975), 185-188
MSC: Primary 41A30; Secondary 41A50
MathSciNet review: 0361555
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Abstract: Let $ {f_1},{f_2}$ be real valued functions on $ [a,b]$ and let $ S$ be a nonempty family of real valued functions on $ [a,b]$. It is shown that the simultaneous approximation of $ {f_1}$ and $ {f_2}$ in the ``sum'' norm by elements of $ S$ is, with one restriction, equivalent to the approximation of the arithmetic mean, $ ({f_1} + {f_2})/2$. A complete characterization of best approximations in the ``sum'' norm is given including results for varisolvent families.

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Keywords: Simultaneous approximation, "sum'' norm, best approximation, arithmetic mean, varisolvent family
Article copyright: © Copyright 1975 American Mathematical Society

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