ABSTRACT
The metric fixed point theory for nonexpansive mappings has its foundations in works of Browder [17], Go¨hde [43], and Kirk [48], published in 1965. Currently, it is known that f.p.p. depends deeply on the norm geometry. In the literature, the reader may find a huge collection of conditions put on the space X or the set C that guarantee possessing the fixed point property. It is not our aim to establish all of them. We rather stress those classical as well as very recent results that are sufficient to understand the topic under discussion. An excellent overview of almost all known facts can be found in the handbook [49].
