Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-18T02:20:35.719Z Has data issue: false hasContentIssue false
  • English
  • Français

Chebyshev Sets in C[0,1] Which are not Suns

Published online by Cambridge University Press:  20 November 2018

Charles B. Dunham
Charles B. Dunham*
Affiliation:
Computer Science DepartmentUniversity of Western Ontario, London, Canada
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Consider approximation of elements of C[0, 1] with respect to the sup-norm by a non-empty subset V of C[0, 1]. Of interest in recent years are subsets V called suns. As C[0, 1] is an MS-space [1, 5], the suns V of C[0, 1] are precisely those subsets V for which each local best approximation is a global best approximation.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 1 , April 1975 , pp. 35 - 37
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Brosowski, B. and Deutsch, F., On some geometrical properties of suns, J. Approx. Theory 10 (1974), 245-267.Google Scholar
2. Dunham, C., Existence and continuity of the Chebyshev operatort SIAM Rev. 10 (1968), 444-446.Google Scholar
3. Dunham, C., Characterization and uniqueness in real Chebyshev approximation, J. Approx. Theory 2 (1969), 374-383.Google Scholar
4. Dunham, C., Partly alternating families, J. Approx. Theory 6 (1972), 378-386.Google Scholar
5. Brosowski, B. and Deutsch, F., Some new continuity concepts for metric projections, Bull. Amer. Math. Soc. 78 (1972), 974-978.Google Scholar
6. Vlasov, L. P., Chebyshev sets in Banach spaces, Sov. Math. Dokl. 2 (1961), 1373-1374.Google Scholar