Simultaneous approximation of a uniformly bounded set of real valued functions (Q1063814)

It is shown that the problem of simultaneous Chebyshev approximation of a set F of bounded, real valued functions on an interval \(| a,b|\) by a non-empty set S of real valued functions is equivalent to the problem of simultaneous approximation of the two functions \(\sup_{f\in F}f\) and \(\inf_{f\in F}f\). The same result is also obtained for simultaneous approximation of f in \(L_ 1\) norm.