Abstract convexity with respect to norm linear functions
Applicable Nonlinear Analysis, Volume 3, Issue 1, April 2026, Pages: 1–7
SAMET BILA
Department of Mathematics, Faculty of Science, Eskisehir Technical University, 26470, Eskisehir, Turkey
REFAIL KASIMBEYLI
Department of Industrial Engineering, Faculty of Engineering, Eskisehir Technical University, 26555, Eskisehir, Turkey
Abstract
In this article, we study abstract convexity, also known as convexity without linearity, for a special class of elementary functions of the form \(\varphi(x)= \langle x^{*},x-a \rangle-c \| x-b\|+\alpha\). Each function \(\varphi(x)\) 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.
Cite this Article as
Samet Bila and Refail Kasimbeyli, Abstract convexity with respect to norm linear functions, Applicable Nonlinear Analysis, 3(1), 1–7, 2026