Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-26T20:31:59.691Z Has data issue: false hasContentIssue false
  • English
  • Français

Centers of Infinite Bounded Sets in a Normed Space

Published online by Cambridge University Press:  20 November 2018

J. R. Calder ,
W. P. Coleman  and
R. L. Harris
J. R. Calder
Affiliation:
Auburn University, Auburn, Alabama; Western Carolina University, Cullowhee, North Carolina
W. P. Coleman
Affiliation:
Auburn University, Auburn, Alabama; Western Carolina University, Cullowhee, North Carolina
R. L. Harris
Affiliation:
Auburn University, Auburn, Alabama; Western Carolina University, Cullowhee, North Carolina
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.

Čebyšev centers have been studied extensively. In this paper an alternate concept of center for infinite bounded point sets is introduced. Some of the results in this paper for this new type of center are similar to previous results for Čebyšev centers.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 5 , October 1973 , pp. 986 - 999
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Day, M. M., James, R. C., and Swaminathan, S., Normed linear spaces that are uniformly convex in every direction, Can. J. Math, (to appear).Google Scholar
2. Day, M. M., Reflexive Banach spaces not isomorphic to uniformly convex spaces, Bull. Amer. Math. Soc. 47 (1941), 313–317.Google Scholar
3. Garkavi, A. L., The best possible net and the best possible cross-section of a set in a normed space, Izv. Akad. Nauk SSSR Ser. Mat. (1962), 87-106.Google Scholar
4. Zizler, V., On some rotundity and smoothness properties of Banach spaces (to appear in Dissertiones Math. Rozprawy Mat.).Google Scholar