Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Best approximation in the space of continuous vector-valued functions
Journal of Approximation Theory
Journal of Approximation Theory
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When G is a finite dimensional Haar subspace of C(X,R^k), the vector-valued continuous functions (including complex-valued functions when k is 2) from a finite set X to Euclidean k-dimensional space, it is well-known that at any function f in C(X,R^k) the best approximation operator satisfies the strong unicity condition of order 2 and a Lipschitz (Holder) condition of order 12. This note shows that in fact the best approximation operator satisfies the usual Lipschitz condition of order 1.