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Title: Best simultaneous $L_p$ approximations (English)
Author: Karakuş, Yusuf
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 48
Issue: 3
Year: 1998
Pages: 457-463
Summary lang: English
Category: math
Summary: In this paper we study simultaneous approximation of $n$ real-valued functions in $L_{p}[ {a,b}]$ and give a generalization of some related results. (English)
Keyword: quasi-metric
Keyword: continuous map
Keyword: Borel map
Keyword: $\sigma $-discrete map
Keyword: $\sigma $-discretely decomposable family
Keyword: absolutely Borel set
Keyword: absolutely analytic space
MSC: 26A21
MSC: 28A05
MSC: 41A28
MSC: 41A50
MSC: 41A65
MSC: 54E35
MSC: 54H05
idZBL: Zbl 0957.41011
idMR: MR1637922
Date available: 2009-09-24T10:15:21Z
Last updated: 2020-07-03
Stable URL:
Reference: [1] A.S.B. Holland and B.N. Sahney: Some remarks on best simultaneous approximation.Theory of Approximation with Application, A.G. Law and B.N. Sahney (eds.), Academic Press, New York, 1976, pp. 332–337. MR 0412694
Reference: [2] W.H. Ling: On simultaneous Chebyshev approximation in the sum norm.Proc. Amer. Mat. Soc. 48 (1975), 185–188. Zbl 0296.41020, MR 0361555
Reference: [3] G.M. Phillips and B.N. Sahney: Best simultaneous approximation in the $L_{{1}}$ and $L_{{2}}$ norms.Theory of Approximation with Applications, A.G. Law and B.N. Sahney (eds.), Academic press, New York, 1976, pp. 213–219. MR 0412693
Reference: [4] A.S.B. Holland, J.H. McCabe, G.M. Phillips and B.N. Sahney: Best simultaneous $L_{{1}}$-approximations.Journal of Approximation Theory 24 (1978), 361–365. MR 0523985, 10.1016/0021-9045(78)90021-7
Reference: [5] Y. Karakuş: Simultaneous approximation in $L_{p}$ norm.Doga-Turkish Journal of Mathematics, Tübitak-Ankara 15 (1991), 25–28. MR 1100817
Reference: [6] Y. Karakuş and S. Atacik: Simultaneous Approximation in $L_{p}[ {a,b}] $ when $p$ is non-integer real number.Doga-Turkish Journal of Mathematics, Tübitak-Ankara 15 (1991), 165–168. MR 1136185


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