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On best simultaneous approximation in normed linear spaces. (English) Zbl 0347.41019


MSC:

41A50 Best approximation, Chebyshev systems
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
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[1] Bacopoulos, A., Non-linear Chebyshev approximation by vector-norms, J. Approximation Theory, 2, 79-84 (1969) · Zbl 0184.08903
[2] Bacopoulos, A., Deux generalisations de l’approximation Tchebitcheff, vérifiant des contraintes d’interpolation, C. R. Acad. Sci. Paris, 270 (8 juin 1970) · Zbl 0195.07301
[3] Bacopoulos, A., On approximation by sums of Chebyshev norms, Numer. Math., 16, 243-247 (1970) · Zbl 0222.65013
[4] Bacopoulos, A.; Gaff, B., On the reduction of a problem of minimization of \(n + 1\) variables to a problem of one variable, SIAM J. Numer. Anal., 8, 97-103 (1971) · Zbl 0222.41011
[5] Bacopoulos, A.; Marsden, M., On a map from the splines into a positive cone, with applications, Aequationes Math., 8, 221-228 (1972) · Zbl 0266.41011
[6] Diaz, J. B.; McLaughlin, H. W., On simultaneous Chebyshev approximation of a set of bounded complex-valued functions, J. Approximation Theory, 2, 419-432 (1969) · Zbl 0186.11203
[7] Diaz, J. B.; McLaughlin, H. W., On simultaneous Chebyshev approximation and Chebyshev approximation with an additive weight function, J. Approximation Theory, 6, 68-71 (1972) · Zbl 0246.41023
[8] Dunham, C. B., Simultaneous Chebyshev approximation of functions on an interval, (Proc. Amer. Math. Soc., 18 (1967)), 472-477 · Zbl 0154.05904
[9] Dunham, C. B., Approximation with respect to sums of Chebyshev norms, Aequationes Math., 8, 267-270 (1972) · Zbl 0251.41009
[10] Goel, D. S.; Holland, A. S.B; Nasim, C.; Sahney, B. N., On best simultaneous approximation in normed linear spaces, Canad. Math. Bull., 17, 4 (1974) · Zbl 0314.41018
[11] D. S. Goel, A. S. B. Holland, C. Nasim, and B. N. Sahney\(L_p\); D. S. Goel, A. S. B. Holland, C. Nasim, and B. N. Sahney\(L_p\) · Zbl 0314.41018
[12] A. S. B. Holland, B. N. Sahney, and J. TzimbalarioJ. Approximation Theory; A. S. B. Holland, B. N. Sahney, and J. TzimbalarioJ. Approximation Theory · Zbl 0435.41016
[13] Ling, W. H.; McLaughlin, H. W.; Smith, M. L., Approximation of random functions, AMS Notices, 22, A-161 (1975)
[14] W. H. Ling, H. W. McLaughlin, and M. L. SmithJ. Approximation Theory; W. H. Ling, H. W. McLaughlin, and M. L. SmithJ. Approximation Theory · Zbl 0372.41015
[15] Phillips, G. M.; Sahney, B. N., Best simultaneous approximation in the \(L_1\) and \(L_2\) norms, (Proceedings of Conference on Theory of Approximation at University of Calgary (August 1975), Academic Press: Academic Press New York), to appear · Zbl 0344.41009
[16] Singer, I., Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces (1970), Springer-Verlag: Springer-Verlag New York · Zbl 0197.38601
[17] Rudin, W., Functional Analysis, McGraw-Hill series in Higher Mathematics (1973) · Zbl 0253.46001
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