Abstract:

We first gave two properties of map class K on  abstract convex spaces, and then used the wellknown coincidence point theorem on abstract convex spaces to discuss the existence problem of fixed points for maps on abstract convex spaces and obtained some new fixed point theorems,  from which  several collectively fixed point theorems were established for a family of maps on a product space of a family of abstract convex spaces.

Key words: abstract convex space, map class K,KC,KO, collectively fixed point theorem, KKM map