Watson, G. A. A characterization of best simultaneous approximations. (English) Zbl 0794.41019 J. Approximation Theory 75, No. 2, 175-182 (1993). Let \(X\) be a compact Hausdorff space and \(Y\) a normed linear space and let \(C(x,y)\) denote the set of all continuous functions from \(X\) to \(Y\), equipped with a norm. The author takes up the problem of approximating a finite number of functions in \(C(x,y)\) simultaneously by a function in a subspace of \(C(x,y)\). The main theorem here is concerned with a characterization of best approximation introduced. As a consequence of his theorem the author obtains a result on best simultaneous approximation by S. Tanimoto [J. Approximation Theory 59, No. 3, 359-361 (1989; Zbl 0697.41014)] involving Chebyshev norm. Reviewer: G.D.Dikshit (Auckland) Cited in 20 Documents MSC: 41A50 Best approximation, Chebyshev systems 41A28 Simultaneous approximation Keywords:Chebyshev norm; subdifferential of a norm; subgradient of a norm; best simultaneous approximation Citations:Zbl 0697.41014 PDFBibTeX XMLCite \textit{G. A. Watson}, J. Approx. Theory 75, No. 2, 175--182 (1993; Zbl 0794.41019) Full Text: DOI