Remarks on strongly Wright-convex functions
Volume 102 / 2011
Annales Polonici Mathematici 102 (2011), 271-278
MSC: Primary 26A51; Secondary 39B62.
DOI: 10.4064/ap102-3-6
Abstract
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.
