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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
DOI: https://doi.org/10.1090/S0002-9939-1975-0361555-4
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.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0361555-4
Keywords: Simultaneous approximation, "sum'' norm, best approximation, arithmetic mean, varisolvent family
Article copyright: © Copyright 1975 American Mathematical Society

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