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Generalized subdifferential of the distance function
Author(s):
S.
Dutta
Journal:
Proc. Amer. Math. Soc.
133
(2005),
2949-2955.
MSC (2000):
Primary 41A65, 41A52;
Secondary 46B20
Posted:
May 9, 2005
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Abstract:
We derive the proximal normal formula for almost proximinal sets in a smooth and locally uniformly convex Banach space. Our technique leads us to show the generic Fréchet smoothness of the distance function in the case the norm is Fréchet smooth, and we derive a necessary and sufficient condition for the convexity of a Chebyshev set in a Banach space  with norms on  and  locally uniformly convex.
References:
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- 1.
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- 2.
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- 3.
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- 5.
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Additional Information:
S.
Dutta
Affiliation:
Stat--Math Division, Indian Statistical Institute, 203, B. T. Road, Kolkata 700 108, India
Address at time of publication:
Department of Mathematics, Ben-Gurion University of the Negev, P.O.B. 653, Beer-Sheva 84105, Israel
Email:
sudipta_r@isical.ac.in, sudipta@math.bgu.ac.il
DOI:
10.1090/S0002-9939-05-08153-0
PII:
S 0002-9939(05)08153-0
Keywords:
Nearest points,
proximinal sets,
almost proximinal sets,
Chebyshev sets,
generalized subdifferential
Received by editor(s):
April 10, 2003
Posted:
May 9, 2005
Communicated by:
Jonathan M. Borwein
Copyright of article:
Copyright
2005,
American Mathematical Society
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