Remarks on strongly Wright-convex functions

Nelson Merentes¹ ; Kazimierz Nikodem² ; Sergio Rivas³

¹ Escuela de Matemáticas Universidad Central de Venezuela Caracas, Venezuela
² Department of Mathematics and Computer Science University of Bielsko-Biała 43-309 Bielsko-Biała, Poland
³ Open National University Caracas, Venezuela

Annales Polonici Mathematici, Tome 102 (2011) no. 3, pp. 271-278

Résumé

Some properties of strongly Wright-convex functions are presented. In particular it is shown that a function $f:D\to \mathbb{R}$, where $D$ is an open convex subset of an inner product space $X$, is strongly Wright-convex with modulus $c$ if and only if it can be represented in the form $f(x)= g(x)+a(x)+c\|x\|^2$, $x \in D$, where $g:D\to \mathbb{R}$ is a convex function and $a:X\to \mathbb{R}$ is an additive function. A characterization of inner product spaces by strongly Wright-convex functions is also given.

Détail

DOI : 10.4064/ap102-3-6

Keywords: properties strongly wright convex functions presented particular shown function mathbb where convex subset inner product space strongly wright convex modulus only represented form where mathbb convex function mathbb additive function characterization inner product spaces strongly wright convex functions given