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

• Autorzy: Dorota Krassowska , Janusz Matkowski
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 26D15: Inequalities for sums, series and integrals
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 39B72: Systems of functional equations and inequalities

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2005
• Tom: 85
• Numer: 1
• Strony: 1-11

Daty

wydano

2005

Twórcy

autor

Dorota Krassowska

• Faculty of Mathematics, Informatics and Econometry, University of Zielona Góra, PL-65-246 Zielona Góra, Poland

autor

Janusz Matkowski

• Faculty of Mathematics, Informatics and Econometry, University of Zielona Góra, PL-65-246 Zielona Góra, Poland
• Institute of Mathematics, Silesian University, PL-40-007 Katowice, Poland

Identyfikatory

DOI

10.4064/ap85-1-1