Extremal function pairs in asymmetric normed linear spaces

In [4] Kemajou et al. constructed the injective hull in the category of T0-quasi-metric spaces with nonexpansive maps that they called q-hyperconvex hull. In this paper, we study properties of functions pairs of the q-hyperconvex hull of asymmetric normed linear spaces. We show, for instance, that any point in the q-hyperconvex hull of an asymmetric normed linear space is convex.