Document Type
Lecture
Publication Date
9-3-2009
Abstract
In this paper, we first introduce the notion of locally uniformly totally convex functions defined on a Banach space and discuss its relations to totally convex, essentially strictly convex, and uniformly convex functions. We then present sufficient conditions for the (norm-weak) upper semicontinuity and (norm-weak) continuity of the Bregman projection operator ������ and the relative projection operator ������ in terms of the notion of ��-approximate (weak) compactness whenever �� is either a locally uniformly totally convex function or coercive, and �� is a nonempty closed subset of int(dom ��). Finally, we present sufficient and equivalent conditions for the convexity of a Chebyshev subset of a Banach space �� in the sense of Bregman distance.
Relational Format
presentation
Recommended Citation
Song, Wen, "Bregman distance, approximate compactness and Chebyshev sets in Banach spaces" (2009). Analysis Seminar. 36.
https://egrove.olemiss.edu/math_analysis/36
