Hostname: page-component-5c6d5d7d68-qks25 Total loading time: 0 Render date: 2024-08-15T19:28:42.846Z Has data issue: false hasContentIssue false
  • English
  • Français

Characterization and uniqueness of nonlinear uniform approximation

Published online by Cambridge University Press:  20 January 2009

Wenshan Yang ,
Chong Li  and
G. A. Watson
Wenshan Yang
Affiliation:
Research Bureau, Zhejiang Normal University, Jinhua City, Zhejiang, P.R. China
Chong Li
Affiliation:
Department of Mathematics, Hangzhou Institute of Commerce, Hangzhou, P.R. China
G. A. Watson
Affiliation:
Department of Mathematics and Computer Science, University of Dundee, Dundee DD1 4HN, ScotlandE-mail address:gawatson@mcs.dundee.ac.uk
Rights & Permissions [Opens in a new window]

Abstract

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.

Characterization and uniqueness results are given for uniform approximation which extend to suns previously known results for convex sets.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 40 , Issue 3 , October 1997 , pp. 473 - 482
Copyright
Copyright © Edinburgh Mathematical Society 1997

References

REFERENCES

1.Amir, D. and Deutch, F., Suns, moons and quasi-polyhedra, J Approx. Theory 6 (1972), 176–201.CrossRefGoogle Scholar
2.Braess, D., Nonlinear Approximation Theory (Springer Verlag, Berlin, 1986).CrossRefGoogle Scholar
3.Brosowski, B., Nichtlineare Approximation in normierten Vectorraumen, in Abstract Spaces and Approximation (eds. Butzer, P. L. and Sz-Nagy, B., ISNM 10, Birkhauser, Basel, 1969), 140–159.CrossRefGoogle Scholar
4.Li Chong, and Watson, G. A., Characterization of a best and a unique best approximation from constrained rationals, Comput. Math. Appl. 30 (1995), 51–57.CrossRefGoogle Scholar
5.Dunham, C. B., Characterizability and uniqueness in real Chebyshev approximation, J. Approx. Theory 2 (1969), 374–383.CrossRefGoogle Scholar
6.Dunham, C. B., Chebyshev approximation by families with the betweeness property, Trans. Amer. Math. Soc. 136 (1969), 151–157.CrossRefGoogle Scholar
7.Nurnberger, G., Unicity and strong unicity in approximation theory, J Approx. Theory 26 (1979), 54–70.CrossRefGoogle Scholar
8.Papini, P. L., Approximation and norm derivatives in real normed spaces, Resultate Math. 5 (1982), 81–94.CrossRefGoogle Scholar
9.Sato, K., On the generators of non-negative contraction semi-groups in Banach spaces, J. Math. Soc. Japan 20 (1968), 420–436.CrossRefGoogle Scholar
10.Vlasov, L. P., Chebyshev sets in Banach Spaces, Soviet Math. Dokl. 2 (1961), 1373–1374.Google Scholar