New generalizations of basic theorems in the KKM theory Original Research Article

In the present paper, we obtain a new KKM type theorem for intersectionally closed-valued KKM maps and some useful new basic consequences. Typical examples of them are abstract forms of Fan’s matching theorem, Fan’s geometric lemma, the Fan–Browder fixed point theorem, maximal element theorems, Fan’s minimax inequality, variational inequalities, and others.