Abstract. Various forms of convexity in normed linear spaces that fall between strict and uniform convexity, such as the 2R property, local uniform convexity, compact local uniform convexity, and mid-point local uniform convexity, have sparked considerable interest over the years and have been thoroughly
investigated in the literature. The notion of strict convexity was extended to
metric linear spaces by Albinus in 1968, and that of uniform convexity by
Ahuja et al. in 1977. In this paper, we extend the other mentioned forms of
convexity to metric linear spaces. We explore the metric linear spaces that
have these properties and establish inter-relationships between these spaces.
We also give a characterization of strictly convex metric linear spaces.