LAUSR

In this article, we introduce and study the concept of hyperconvexity (which we call $$q^\lambda $$qλ-hyperconvexity) that is appropriate in the category of $$T_0$$T0-quasi-metric spaces and nonexpansive maps and this will generalize the notion of q-hyperconvexity studied by Kemajou et al. We prove a fixed point result for nonexpansive maps in $$q^\lambda $$qλ-hyperconvex spaces and establish, among other things, that the fixed point set of nonexpansive maps on $$q^\lambda $$qλ-hyperconvex bounded $$T_0$$T0-quasi-metric spaces is itself $$q^\lambda $$qλ-hyperconvex.