Best simultaneous $L_p$ approximations
Czechoslovak Mathematical Journal, Tome 48 (1998) no. 3, pp. 457-463 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 26A21, 28A05, 41A28, 41A50, 41A65, 54E35, 54H05
Keywords: quasi-metric; continuous map; Borel map; $\sigma $-discrete map; $\sigma $-discretely decomposable family; absolutely Borel set; absolutely analytic space
@article{CMJ_1998_48_3_a6,
     author = {Karaku\c{s}, Yusuf},
     title = {Best simultaneous $L_p$ approximations},
     journal = {Czechoslovak Mathematical Journal},
     pages = {457--463},
     year = {1998},
     volume = {48},
     number = {3},
     mrnumber = {1637922},
     zbl = {0957.41011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_1998_48_3_a6/}
}
TY  - JOUR
AU  - Karakuş, Yusuf
TI  - Best simultaneous $L_p$ approximations
JO  - Czechoslovak Mathematical Journal
PY  - 1998
SP  - 457
EP  - 463
VL  - 48
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CMJ_1998_48_3_a6/
LA  - en
ID  - CMJ_1998_48_3_a6
ER  - 
%0 Journal Article
%A Karakuş, Yusuf
%T Best simultaneous $L_p$ approximations
%J Czechoslovak Mathematical Journal
%D 1998
%P 457-463
%V 48
%N 3
%U http://geodesic.mathdoc.fr/item/CMJ_1998_48_3_a6/
%G en
%F CMJ_1998_48_3_a6
Karakuş, Yusuf. Best simultaneous $L_p$ approximations. Czechoslovak Mathematical Journal, Tome 48 (1998) no. 3, pp. 457-463. http://geodesic.mathdoc.fr/item/CMJ_1998_48_3_a6/

[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

[2] W.H. Ling: On simultaneous Chebyshev approximation in the sum norm. Proc. Amer. Mat. Soc. 48 (1975), 185–188. | MR | Zbl

[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

[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. | DOI | MR

[5] Y. Karakuş: Simultaneous approximation in $L_{p}$ norm. Doga-Turkish Journal of Mathematics, Tübitak-Ankara 15 (1991), 25–28. | MR

[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