Nearest Points and Delta Convex Functions in Banach Spaces
نویسندگان
چکیده
Given a closed set C in a Banach space (X, ‖ · ‖), a point x ∈ X is said to have a nearest point in C if there exists z ∈ C such that dC(x) = ‖x − z‖, where dC is the distance of x from C. We shortly survey the problem of studying the size of the set of points in X which have nearest points in C. We then turn to the topic of delta-convex functions and indicate how it is related to finding nearest points. 2010 Mathematics subject classification: primary 46B10; secondary 41A29.
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تاریخ انتشار 2015