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>

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...