Some Remarks on Convexity of Čebyšev Sets
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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.
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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
References
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J. M. Borwein, Proximality and Čebyšev sets, Optim. Lett., 1 (2007), 21--32
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J. M. Borwein, S. P. Fitzpatrick, J. R. Giles, , J. Math. Anal. Appl., 128 (1987), 512--534
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J. R. Giles, Convex analysis with applications in differentiation of convex functions, Pitman, London (1982)
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G. G. Johnson, A nonconvex set which has the unique nearest point property, J. Approx. Theory, 51 (1987), 289--332