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 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...