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Unicity in the uniform approximation of vector-valued functions

Published online by Cambridge University Press:  17 April 2009

Lee W. Johnson
Lee W. Johnson
Affiliation:
Virginia Polytechnic Institute and State University, Blacksburg, Virginia, USA.
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Abstract

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The problem of unicity in the uniform approximation of vector-valued functions is considered. A recent result of Cheney and Wulbert concerning unicity in the uniform approximation of real-valued functions is extended and some “point-wise” criteria for unicity are given.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 3 , Issue 2 , October 1970 , pp. 193 - 198
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Cheney, E:W. and Wulbert, D.E., “The existence and unicity of best approximations”, Math. Scand. 24 (1969), 113–140.CrossRefGoogle Scholar
[2]Eggleston, H.G., Convexity (Cambridge Tracts in Mathematics and Mathematical Physics, no. 47. Cambridge University Press, Cambridge, 1958).CrossRefGoogle Scholar
[3]Collatz, L., “Inclusion theorems for the minimal distance in rational Tschebyscheff approximation with several variables”, Proc. Sympos. General Motors Res. Lab. (1964), 43–56. Approximation of functions, edited by Garabedian, Henry L. (Elsevier Publishing Co., Amsterdam, London, New York, 1965).Google Scholar
[4]Johnson, Lee W., “Uniform approximation of vector-valued functions”, Numer. Math. 13 (1969), 238–244.CrossRefGoogle Scholar