# Wydawnictwa / Czasopisma IMPAN / Annales Polonici Mathematici / Wszystkie zeszyty

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

### Tom 85 / 2005

Annales Polonici Mathematici 85 (2005), 1-11 MSC: Primary 39B72, 26D15; Secondary 46E30. DOI: 10.4064/ap85-1-1

#### Streszczenie

It is shown that, under some general algebraic conditions on fixed real numbers $a,b,\alpha ,\beta$, every solution $f:\mathbb{R}\rightarrow \mathbb{R}$ of the system of functional inequalities $f(x+a)\leq f(x)+\alpha ,$ $f(x+b)\leq f(x)+\beta$ 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.

#### Autorzy

• Dorota KrassowskaFaculty of Mathematics, Informatics and Econometry
University of Zielona Góra
PL-65-246 Zielona Góra, Poland
e-mail
• Janusz MatkowskiFaculty of Mathematics, Informatics and Econometry
University of Zielona Góra
PL-65-246 Zielona Góra, Poland
and
Institute of Mathematics
Silesian University
PL-40-007 Katowice, Poland
e-mail

## Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek