Approximation of lipschitz functions by Δ-convex functions in banach spaces
نویسندگان
چکیده
منابع مشابه
Uniformly Convex Functions on Banach Spaces
We study the connection between uniformly convex functions f : X → R bounded above by ‖ · ‖p, and the existence of norms on X with moduli of convexity of power type. In particular, we show that there exists a uniformly convex function f : X → R bounded above by ‖ · ‖2 if and only if X admits an equivalent norm with modulus of convexity of power type 2.
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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 neare...
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 1998
ISSN: 0021-2172,1565-8511
DOI: 10.1007/bf02773472