Generalizations of the KKM type theorems on generalized convex spaces

We establish a new KKM theorem related to multimaps in the admissible class A(c)(kappa) defined on generalized convex spaces and extend it for transfer compactly closed-valued multimaps. Using this obtained are a whole intersection property, a coincidence theorem, an equilibrium theorem, and the Ky Fan type matching theorem for open covers as applications.