An overview on the Prus-Szczepanik condition

In 2005 Prus and Sczcepanik introduced a large class of Banach spaces with the fixed point property for nonexpansive mappings. We say that this class satisfies the PSz condition. Checking that a given Banach space belongs to this class is not an easy task. Here we study the relationship between the PSz condition and other well-known geometrical properties of Banach spaces, and we give easier sufficient conditions for a Banach space to satisfy it.Consejo Nacional de Ciencia y Tecnologia (México)Ministerio de Economía y Competitivida