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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On simultaneous Chebyshev approximation in the “sum” norm
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by William H. Ling PDF
Proc. Amer. Math. Soc. 48 (1975), 185-188 Request permission

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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Additional Information
  • © Copyright 1975 American Mathematical Society
  • 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