Convexity and Geodesic Metric Spaces

Abstract

In this paper, we first present a preliminary study on metric segments and geodesics in metric spaces. Then we recall the concept of d-convexity of sets and functions in the sense of Menger and study some properties of d-convex sets and d-convex functions as well as extreme points and faces of d-convex sets in normed spaces. Finally we study the continuity of d-convex functions in geodesic metric spaces. ./files/site1/files/71/7.pdf

Keywords

•  geodesic
• metric segment
• d-convex set
• metric convex hull
• d-convex function
• extreme point
• continuity.