Remarks on strongly Wright-convex functions

Nelson Merentes, Kazimierz Nikodem, and Sergio Rivas. "Remarks on strongly Wright-convex functions." Annales Polonici Mathematici 102.3 (2011): 271-278. <http://eudml.org/doc/280352>.

@article{NelsonMerentes2011,
abstract = {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.},
author = {Nelson Merentes, Kazimierz Nikodem, Sergio Rivas},
journal = {Annales Polonici Mathematici},
keywords = {strongly convex functions; strongly Wright-convex functions; inner product spaces},
language = {eng},
number = {3},
pages = {271-278},
title = {Remarks on strongly Wright-convex functions},
url = {http://eudml.org/doc/280352},
volume = {102},
year = {2011},
}

TY - JOUR
AU - Nelson Merentes
AU - Kazimierz Nikodem
AU - Sergio Rivas
TI - Remarks on strongly Wright-convex functions
JO - Annales Polonici Mathematici
PY - 2011
VL - 102
IS - 3
SP - 271
EP - 278
AB - 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.
LA - eng
KW - strongly convex functions; strongly Wright-convex functions; inner product spaces
UR - http://eudml.org/doc/280352
ER -