ABSTRACT CONVEXITY WITH RESPECT TO NORM LINEAR FUNCTIONS

Bila S., Kasımbeyli R.

Applicable Nonlinear Analysis, vol.3, no.1, pp.1-7, 2026 (Scopus) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 3 Say: 1
  • Nəşr tarixi: 2026
  • Doi nömrəsi: 10.69829/apna-026-0301-ta01
  • jurnalın adı: Applicable Nonlinear Analysis
  • Jurnalın baxıldığı indekslər: Scopus
  • Səhifə sayı: pp.1-7
  • Açar sözlər: Abstract convexity, Nonconvex analysis, Weak subdifferential
  • Adres: Bəli

Qısa məlumat

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.