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 be real valued functions on and let be a nonempty family of real valued functions on . It is shown that the simultaneous approximation of and in the ``sum'' norm by elements of is, with one restriction, equivalent to the approximation of the arithmetic mean, . A complete characterization of best approximations in the ``sum'' norm is given including results for varisolvent families.

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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