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On Best Simultaneous Approximation in Normed Linear Spaces

Published online by Cambridge University Press:  20 November 2018

D. S. Goel ,
A. S. B. Holland ,
C. Nasim  and
B. N. Sahney
D. S. Goel
Affiliation:
Department of Mathematics, The University of Calgary, Calgary, Alberta, T2N 1N4, Canada
A. S. B. Holland
Affiliation:
Department of Mathematics, The University of Calgary, Calgary, Alberta, T2N 1N4, Canada
C. Nasim
Affiliation:
Department of Mathematics, The University of Calgary, Calgary, Alberta, T2N 1N4, Canada
B. N. Sahney
Affiliation:
Department of Mathematics, The University of Calgary, Calgary, Alberta, T2N 1N4, Canada
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Let S be a non-empty family of real valued continuous functions on [a, b]. Diaz and McLaughlin [1], [2], and Dunham [3] have considered the problem of simultaneously approximating two continuous functions f1 and f2 by elements of S. If || • || denotes the supremum norm, then the problem is to find an element * ∈ S if it exists, for which

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 4 , 01 December 1974 , pp. 523 - 527
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Diaz, J. B. and McLaughlin, H. W., Simultaneous approximation of a set of bounded functions, Math. Comp. 23 (1969), pp. 583-594.Google Scholar
2. Diaz, J. B. and McLaughlin, H. W., On simultaneous Chebyshev approximation and Chebyshev approximation with an additive weight function, J. App. Theory 6 (1972), pp. 68-71.Google Scholar
3. Dunham, C. B., Simultaneous Chebyshev approximation of functions on an interval, Proc. Amer. Math. Soc. 18 (1967), pp. 472-477.Google Scholar