Abstract:

The concept of an abstact convex space without any topological structure was introduced, and fixed point theorems, matching theorems and whole intersection theorems were obtained on the basis of the well known coincidence point theorem on an abstract convex space, which is adequate to establish the KKM theory, and then  another type of coincidence theorem was given via obtained fixed point theorem. These results generalize and simplify the corresponding known results in the KKM theory on convex spaces, H-spaces, G-convex spaces, and others.

Key words: abstract convex space, map classes R,RC,RD, fixed point, matching