It is shown that, under some general algebraic conditions on fixed real numbers a,b,α,β, every solution f:ℝ → ℝ of the system of functional inequalities f(x+a) ≤ f(x)+α, f(x+b) ≤ f(x)+β that is continuous at some point must be a linear function (up to an additive constant). Analogous results for three other similar simultaneous systems are presented. An application to a characterization of -norm is given.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap85-1-1,
author = {Dorota Krassowska and Janusz Matkowski},
title = {A pair of linear functional inequalities and a characterization of $L^{p}$-norm},
journal = {Annales Polonici Mathematici},
volume = {85},
year = {2005},
pages = {1-11},
zbl = {1085.39025},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap85-1-1}
}
Dorota Krassowska; Janusz Matkowski. A pair of linear functional inequalities and a characterization of $L^{p}$-norm. Annales Polonici Mathematici, Tome 85 (2005) pp. 1-11. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap85-1-1/