ABSTRACT
N. Aronszajn and P. Panitchpakdi introduced hyperconvex metric spaces in 1956 ([1]) when studying the problem of extending uniformly continuous mapping between metric spaces. The recent interest of fixed point theory in hyperconvex spaces goes back to results of Sine [16] and Soardi [17] who independently proved that the fixed point property for nonexpansive mappings holds in bounded hyperconvex spaces. Since then many different results have been shown to hold in hyperconvex spaces, and very recently many of them were stated under noncompactness conditions (see for instance [6], [9], [10] and [12]).
