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JAT
2010

The Bregman distance, approximate compactness and convexity of Chebyshev sets in Banach spaces

9 years 8 months ago
The Bregman distance, approximate compactness and convexity of Chebyshev sets in Banach spaces
We present some sufficient conditions ensuring the upper semicontinuity and the continuity of the Bregman projection operator Π g C and the relative projection operator P g C in terms of the D-approximate (weak) compactness for a nonempty closed set C in a Banach space X. We next present certain sufficient conditions as well as equivalent conditions for the convexity of a Chebyshev subset of a Banach space X. Our results extend the corresponding results of [H.H. Bauschke, X.F. Wang, J. Ye and X. M. Yuan, Bregman distances and Chebyshev sets, J. Approx. Theory 159 (2009) 3–25] to infinite dimensional spaces. c 2010 Published by Elsevier Inc.
Chong Li, Wen Song, Jen-Chih Yao
Added 28 Jan 2011
Updated 28 Jan 2011
Type Journal
Year 2010
Where JAT
Authors Chong Li, Wen Song, Jen-Chih Yao
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