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Mathematics of Computation

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Simultaneous approximation of a set of bounded real functions

Authors: J. B. Diaz and H. W. McLaughlin
Journal: Math. Comp. 23 (1969), 583-593
MSC: Primary 41.40
MathSciNet review: 0248481
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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.

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Article copyright: © Copyright 1969 American Mathematical Society