Research Information System
Applicable Nonlinear Analysis, vol.3, no.1, pp.1-7, 2026 (Scopus)
In this article, we study abstract convexity, also known as convexity without linearity, for a special class of elementary functions of the form φ(x) = ⟨x∗, x − a⟩ − c∥x − b∥ + α. Each function φ(x) is characterized by a pair (x∗, c), and the class is defined in terms of such pairs. Within the framework of abstract convexity, probably such a characterization arises first. In this work, we define the class of functions that are representable as a pointwise supremum of this family and investigate its properties.