We introduce the concept of λ-hyperconvexity in metric spaces, generalizing the classical notion of a hyperconvex metric space. We show that a bounded metric space which is λ-hyperconvex has the fixed point property for nonexpansive mappings provided λ < 2. Uniformly convex Banach spaces are examples of such λ-hyperconvex spaces for some λ < 2. We furthermore investigate the relationship betwee...

We investigate which represented spaces enjoy the fixed-point property, is property that every continuous multi-valued function has a fixed-point. study basic theory of this notion and its uniform version. provide complete characterization countable-based T0-spaces with showing they are exactly pointed ω-continuous dcpos. prove whose lattice open sets enjoys countably-based spaces. While role p...