Fixed point and equilibrium theorems in pseudoconvex and related spaces

Convexity spaces defined in the paper are generated by families of continuo us functions. Without imposing any explicitly stated linear structure on th e spaces, Browder's, Brouwer's and Kakutani's fixed point theorems are prov ed and used for deriving generalized Fan inequalities and two-function mini max theorems. The existence of Nash equilibria in noncooperative games is a lso established under more general conditions than known before. The convex ity spaces studied in the paper allow for unusual (generalized) convex sets and functions.