A pair of linear functional inequalities and a characterization of $L^p$-norm

Dorota Krassowska, and Janusz Matkowski. "A pair of linear functional inequalities and a characterization of $L^{p}$-norm." Annales Polonici Mathematici 85.1 (2005): 1-11. <http://eudml.org/doc/280491>.

@article{DorotaKrassowska2005,
abstract = {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 $L^\{p\}$-norm is given.},
author = {Dorota Krassowska, Janusz Matkowski},
journal = {Annales Polonici Mathematici},
keywords = {functional inequalities; subadditive functions; theorem of Kronecker; -norm-like functional; subhomogeneity; characterization of -norm},
language = {eng},
number = {1},
pages = {1-11},
title = {A pair of linear functional inequalities and a characterization of $L^\{p\}$-norm},
url = {http://eudml.org/doc/280491},
volume = {85},
year = {2005},
}

TY - JOUR
AU - Dorota Krassowska
AU - Janusz Matkowski
TI - A pair of linear functional inequalities and a characterization of $L^{p}$-norm
JO - Annales Polonici Mathematici
PY - 2005
VL - 85
IS - 1
SP - 1
EP - 11
AB - 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 $L^{p}$-norm is given.
LA - eng
KW - functional inequalities; subadditive functions; theorem of Kronecker; -norm-like functional; subhomogeneity; characterization of -norm
UR - http://eudml.org/doc/280491
ER -