In this paper we discuss necessary and sufficient conditions for different minimax results to hold using only linear programming duality and the finite intersection property of compact sets. It turns out that these necessary and sufficient conditions have a clear interpretation within zero-sum...

In this paper we review and unify some of the classes of generalized convex functions introduced by different authors to prove minimax results in infinite dimensional spaces and show the relations between those classes. We also list for the most general class already introduced by Jeyakumar an...

In this paper which will appear as a chapter in the Handbook of Generalized Convexity we discuss the basic ideas of convex and quasiconvex analysis in finite dimensional Euclidean spaces. To illustrate the usefulness of this branch of mathematics also applications to optimization theory and...

In this note we review some known minimax theorems with applications in game theory and show that these results form an equivalent chain which includes the strong separation result in finite dimensional spaces between two disjoint closed convex sets of which one is compact. By simplifying the...

In this paper we introduce several classes of generalized convex functions already discussed in the literature and show the relation between those function classes. Moreover, for some of those function classes a Farkas-type theorem is proved. As such this paper unifies and extends results...

In this chapter we give an overview on the theory of noncooperative games. In the first part we consider in detail for zero-sum (and constant-sum) noncooperative games under which necessary and sufficient conditions on the payoff function and different (extended) strategy sets for both players...

We consider infinite products of the form (see article). We show that (see article) can decrease at infinity not faster than (see article) and present conditions under which this maximal decay attains. This result proves the impossibility of the construction of infinitely differentiable...

We consider a univariate two-scale difference equation, which is studied in approximation theory, curve design and wavelets theory. This paper analysis the correlation between the existence of smooth compactly supported solutions of this equation and the convergence of the corresponding cascade...

The paper analysis the correlation between the existence of smooth compactly supported solutions of the univariate two-scale refinement equation and the convergence of the corresponding cascade lgorithm/subdivision scheme. We introduce a criterion that expresses this correlation in terms of mask...

In this paper we investigate the tail behaviour of a random variable S which may be viewed as a functional T of a zero mean Gaussian process X, taking special interest in the situation where X obeys the structure which is typical for limiting processes ocurring in nonparametric testing of...