Some Remarks on Convexity of Čebyšev Sets

Volume 1, Issue 2, pp 102--106 http://dx.doi.org/10.22436/jmcs.001.02.05

Download PDF

Download XML

2166 Downloads
3674 Views

Authors

Hossein Asnaashari - Faculty of basic sciences, Zabol University, Zabol, Iran

Abstract

In this paper, we study a part of approximation theory that presents the conditions under which a Čebyšev set in a Banach space is convex. To do so, we use Gateaux differentiability of the distance function.

Share and Cite

ISRP Style

Hossein Asnaashari, Some Remarks on Convexity of Čebyšev Sets, Journal of Mathematics and Computer Science, 1 (2010), no. 2, 102--106

AMA Style

Asnaashari Hossein, Some Remarks on Convexity of Čebyšev Sets. J Math Comput SCI-JM. (2010); 1(2):102--106

Chicago/Turabian Style

Asnaashari, Hossein. "Some Remarks on Convexity of Čebyšev Sets." Journal of Mathematics and Computer Science, 1, no. 2 (2010): 102--106

Keywords

Distance function
nearest point
Cebyšev set
strictly convex space
smooth space
Gateaux differentiability.

MSC

46B20
41A50
46N10
49J50

References

[1] V. S. Balaganski, L. P. Vlasov, The problem of the convexity of Čebyšev sets, Russian Math. Surveys, 51 (1996), 1127--1190
- View Article
- Google Scholar

[2] J. M. Borwein, Proximality and Čebyšev sets, Optim. Lett., 1 (2007), 21--32

[3] J. M. Borwein, S. P. Fitzpatrick, J. R. Giles, , J. Math. Anal. Appl., 128 (1987), 512--534

[4] J. R. Giles, Convex analysis with applications in differentiation of convex functions, Pitman, London (1982)

[5] G. G. Johnson, A nonconvex set which has the unique nearest point property, J. Approx. Theory, 51 (1987), 289--332