In this paper, we investigate abstract convexity of non-positive increasing and radiant (IR) functions over a topological vector space. We characterize the essential results of abstract convexity such as support set, subdifferential and polarity of these functions. We also give some...

In this paper, we first obtain some properties of topical (increasing and plus-homogeneous) functions in the framework of abstract convexity. Next, we use the Toland–Singer formula to characterize the dual problem for the difference of two topical functions. Finally, we present necessary and...

An open question in the study of quasiconvex function is the characterization of the class of functions which are sum of quasiconvex functions. In this paper we restrict our attention to quasiconvex radiant functions, i.e. those whose level sets are radiant as well as convex and deal with the...

In this paper, we examine properties of topical (increasing and plus-homogeneous) functions defined on a normed linear space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${X}$$</EquationSource> </InlineEquation>. We also study many results of abstract convexity such as support set, polarity and subdifferential set of these functions. Finally, we give a characterization...</equationsource></inlineequation>

We study increasing quasiconcave functions which are co-radiant. Such functions have frequently been employed in microeconomic analysis. The study is carried out in the contemporary framework of abstract convexity and abstract concavity. Various properties of these functions are derived. In...

In a linear contracting environment the Fenchel transform provides a complete duality between the contract and the information rent. Through an appropriate generalised convexity this can be extended to provide a complete duality in the supermodular quasilinear contracting environment that covers...

An open question in the study of quasiconvex function is the characterization of the class of functions which are sum of quasiconvex functions. In this paper we restrict our attention to quasiconvex radiant functions, i.e. those whose level sets are radiant as well as convex and deal with the...

The aim of this paper is twofold. On the one hand to present by means of a unique statement an existence result which covers both ways (convexity and acyclicity) of analyzing the problem of existence of maximal elements of non transitive binary relations. And on the other hand, to introduce the...

We suggest a concept of convexity of preferences that does not rely on any algebraic structure. A decision maker has in mind a set of orderings interpreted as evaluation criteria. A preference relation is defined to be convex when it satisfies the following: if for each criterion there is an...