In this paper the well-known minimax theorems of Wald, Ville and Von Neumann are generalized under weaker topological conditions onthe payoff function ƒ and/or extended to the larger set of the Borel probabilitymeasures instead of the set of mixed strategies.

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...

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...

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...

In this paper we give a short novel proof of the well-known Lagrange multiplier rule, discuss the sources of the power of this rule and consider several applications of this rule. The new proof does not use the implicit function theorem and combines the advantages of two of the most well-known...

We present the Lagrange multiplier rule, one of the basic optimization methods, in a new way. Novel features include: • Explanation of the true source of the power of the rule: reversal of tasks, but not the use of multipliers. • A natural proof based on a simple picture, but not the usual...

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...

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 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 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...