The present paper is divided into two parts. In the first part,
we derive a Fan-KKM type theorem and establish some Fan type geometric
properties of convex spaces. By applying our results, we also
obtain some coincidence theorems and fixed-point theorems in the setting
of convex spaces. The second part deals with the applications of our
coincidence theorem to establish some existence results for a solution to
the generalized vector equilibrium problems.
Journal of Optimization Theory and Applications, 117(1):121-137