# Article

Full entry | PDF   (0.2 MB)
Keywords:
quasi-metric; continuous map; Borel map; $\sigma$-discrete map; $\sigma$-discretely decomposable family; absolutely Borel set; absolutely analytic space
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.
References:
[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
[2] W.H. Ling: On simultaneous Chebyshev approximation in the sum norm. Proc. Amer. Mat. Soc. 48 (1975), 185–188. MR 0361555 | Zbl 0296.41020
[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
[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
[5] Y. Karakuş: Simultaneous approximation in $L_{p}$ norm. Doga-Turkish Journal of Mathematics, Tübitak-Ankara 15 (1991), 25–28. MR 1100817
[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

Partner of