We prove Kolmogorov's type characterization of best approximation for given \(L \in \mathscr{L}(W, V)\) in finite dimensional subspace \(\mathscr{V} \subset \mathscr{L}(W, V)\). This extends the results obtained by Malbrock for the case \(W=V=c_{0}\) and \(W=C(T), V=C(S)\). co 1995 Academic Press, I
On Best Polynomial Approximation in L2W(S)
โ Scribed by Z. Ditzian
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 332 KB
- Volume
- 194
- Category
- Article
- ISSN
- 0022-247X
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๐ SIMILAR VOLUMES
Let f ยฅ C 2, 2 ([ -1, 1] 2 ) be a real function satisfying " 4 f/"x 2 "y 2 \ 0 on [ -1, 1] 2 . We study the problem of best one-sided L 1 -approximation to f from the linear space {h ยฅ C 2, 2 ([ -1, 1] 2 ) : " 4 h/"x 2 "y 2 =0} of all blending functions of order (2, 2). The unique best one-sided L 1
## Abstract In this paper the concepts of strictly convex and uniformly convex normed linear spaces are extended to metric linear spaces. A relationship between strict convexity and uniform convexity is established. Some existence and uniqueness theorems on best approximation in metric linear space