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...

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...

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 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...