On Best Simultaneous Approximation in Normed Linear Spaces

Abstract

Let S be a non-empty family of real valued continuous functions on [a, b]. Diaz and McLaughlin [1], [2], and Dunham [3] have considered the problem of simultaneously approximating two continuous functions f1 and f2 by elements of S. If || • || denotes the supremum norm, then the problem is to find an element * ∈ S if it exists, for which