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## Remarks on strongly Wright-convex functions

### Tom 102 / 2011

Annales Polonici Mathematici 102 (2011), 271-278 MSC: Primary 26A51; Secondary 39B62. DOI: 10.4064/ap102-3-6

#### Streszczenie

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.

#### Autorzy

• Nelson MerentesEscuela de Matemáticas
Caracas, Venezuela
e-mail
• Kazimierz NikodemDepartment of Mathematics and Computer Science
University of Bielsko-Biała
43-309 Bielsko-Biała, Poland
e-mail
• Sergio RivasOpen National University
Caracas, Venezuela
e-mail

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