Nearest Points and Delta Convex Functions in Banach Spaces

Abstract

Abstract. 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 d C (x) = x − z , where d C is the distance of x from C. We shortly survey the problem of studying how large is the set of points in X which have nearest points in C. We then discuss the topic of delta-convex functions and how it is related to finding nearest points.