Simultaneous approximation of a set of bounded real functions

Diaz, J. B.; McLaughlin, H. W.

doi:10.1090/S0025-5718-1969-0248481-1

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

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Simultaneous approximation of a set of bounded real functions
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by J. B. Diaz and H. W. McLaughlin PDF

Math. Comp. 23 (1969), 583-593 Request permission

Abstract:

The problem of simultaneous Chebyshev approximation of a set $F$ of uniformly bounded, real-valued functions on a compact interval $I$. by a set $P$ of continuous functions is equivalent to the problem of simultaneous approximation of two real-valued functions ${F^ + }(x),{F^ - }(x)$, with ${F^ - }(x) \leqq {F^ + }(x)$, for all $x$ in $I$, where ${F^ - }$ is lower semicontinuous and ${F^ - }$ is upper semicontinuous.

References

Charles B. Dunham, Simultaneous Chebyshev approximation of functions on an interval, Proc. Amer. Math. Soc. 18 (1967), 472–477. MR 212463, DOI 10.1090/S0002-9939-1967-0212463-6