In this paper we introduce several classes of generalized convexfunctions already discussed in the literature and show the relationbetween those function classes. Moreover, for some of those functionclasses a Farkas-type theorem is proved. As such this paper unifiesand extends results existing...

In this paper we review known minimax results with applications in game theory and show that these results are easy consequences of the first minimax result for a two person zero sum game with finite strategy sets published by von Neumann in 1928: Among these results are the well known minimax...

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...

We consider a class of homogeneous Cournot oligopolies with concave integrated price flexibility and convex cost functions. We provide new results about the semi-uniqueness and uniqueness of (Cournot) equilibria for the oligopolies that satisfy these conditions. The condition of concave...

The problem of minimizing $${\tilde f=f+p}$$ over some convex subset of a Euclidean space is investigated, where f(x) = x T Ax + b T x is strictly convex and |p| is only assumed to be bounded by some positive number s. It is shown that the function $${\tilde f}$$ is strictly outer γ-convex...

A real-valued function f defined on a convex subset D of some normed linear space is said to be inner γ-convex w.r.t. some fixed roughness degree γ    0 if there is a $$\nu \in]0, 1]$$ such that $${\rm sup}_{\lambda\in[2,1+1/\nu]} \left(f((1 - \lambda)x_0 + \lambda x_1) - (1 - \lambda) f...

A nonsmooth multiobjective optimization problem involving generalized (F, α, ρ, d)-type I function is considered. Karush–Kuhn–Tucker type necessary and sufficient optimality conditions are obtained for a feasible point to be an efficient or properly efficient solution. Duality results are...

The problem of minimizing <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${\tilde f=f+p}$$</EquationSource> </InlineEquation> over some convex subset of a Euclidean space is investigated, where f(x) = x <Superscript> T </Superscript> Ax + b <Superscript> T </Superscript> x is strictly convex and |p| is only assumed to be bounded by some positive number s. It is shown that the function <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${\tilde f}$$</EquationSource> </InlineEquation> is strictly outer...</equationsource></inlineequation></superscript></superscript></equationsource></inlineequation>