On Strongly Convex Sets and Farthest Distance Functions
Functional Analysis
2025-08-05 v2 Optimization and Control
Abstract
A polarity notion for sets in a Banach space is introduced in such a way that the second polar of a set coincides with the smallest strongly convex set with respect to R that contains it. Strongly convex sets are characterized in terms of their associated farthest distance functions, and farthest distance functions associated with strongly convex sets are characterized, too.
Keywords
Cite
@article{arxiv.2507.15053,
title = {On Strongly Convex Sets and Farthest Distance Functions},
author = {Juan Enrique Martínez-Legaz},
journal= {arXiv preprint arXiv:2507.15053},
year = {2025}
}