The Bregman distance, approximate compactness and convexity of Chebyshev sets in Banach spaces
نویسندگان
چکیده
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 Elsevier Inc. All rights reserved.
منابع مشابه
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 ΠgC 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 Ba...
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ورودعنوان ژورنال:
- Journal of Approximation Theory
دوره 162 شماره
صفحات -
تاریخ انتشار 2010