Journal of the
Korean Mathematical Society JKMS

In [11] Kim obtained fixed point theorems for maps defined on some ``locally $G$-convex'' subsets of a generalized convex space. Theorem 2 in Kim's article determines us to introduce, in this paper, the notion of $K$-$% G $-convex space. In this framework we obtain fixed point theorems, section properties and minimax inequalities.

Keywords: generalized convex space, $K$-$G$-convex space, map, Kakutani map, selection, section property, minimax inequality

MSC numbers: 54H25, 54C60, 47H10