radially convex at

Given a continuum X with an arc-structure A and a point $p \in X$, a metric d on X is said to be radially convex at p provided that d(p,z) = d(p,y) + d(y,z) for every points $y, z \in X$ with $y \in A(p,z)$ (see [42, I.4, p. 551]).