Some properties of strongly Wright-convex functions are presented. In particular it is shown that a function f:D → 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 ∈ D, where g:D → ℝ is a convex function and a:X → ℝ is an additive function. A characterization of inner product spaces by strongly Wright-convex functions is also given.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap102-3-6,
author = {Nelson Merentes and Kazimierz Nikodem and Sergio Rivas},
title = {Remarks on strongly Wright-convex functions},
journal = {Annales Polonici Mathematici},
volume = {101},
year = {2011},
pages = {271-278},
zbl = {1229.26021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap102-3-6}
}
Nelson Merentes; Kazimierz Nikodem; Sergio Rivas. Remarks on strongly Wright-convex functions. Annales Polonici Mathematici, Tome 101 (2011) pp. 271-278. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap102-3-6/