On Strongly Convex Sets and Farthest Distance Functions

2025/07/20 by Juan Enrique Martínez-Legaz, Martínez-Legaz, Juan Enrique
Computer Science · Mathematics · #26B25 #52A05 #Advanced Optimization Algorithms Research #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2507.15053

openalex publication_date 2025/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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