Geodesic
A pair of linear functional inequalities and a characterization of $L^{p}$-norm
Dorota Krassowska1 ; Janusz Matkowski2
1 Faculty of Mathematics, Informatics and Econometry University of Zielona Góra PL-65-246 Zielona Góra, Poland
2 Faculty 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
Annales Polonici Mathematici, Tome 85 (2005) no. 1, pp. 1-11 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ap85-1-1
Keywords: shown under general algebraic conditions fixed real numbers alpha beta every solution mathbb rightarrow mathbb system functional inequalities leq alpha leq beta continuous point linear function additive constant analogous results three other similar simultaneous systems presented application characterization norm given

Dorota Krassowska 1 ; Janusz Matkowski 2

1 Faculty of Mathematics, Informatics and Econometry University of Zielona Góra PL-65-246 Zielona Góra, Poland
2 Faculty 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 
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Dorota Krassowska; Janusz Matkowski. A pair of linear functional inequalities
and a characterization of  $L^{p}$-norm. Annales Polonici Mathematici, Tome 85 (2005) no. 1, pp. 1-11. doi: 10.4064/ap85-1-1

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