On probability distribution solutions of a functional equation

• Autorzy: Morawiec J. , Reich L.

Identyfikatory

DOI

10.4064/ba53-4-4

• Języki publikacji: EN

Abstrakty

EN

Let 0 < β < α < 1 and let p ∈ (0,1). We consider the functional equation [WZÓR] and its solutions in two classes of functions, namely Z ={φ: R→ R∣ φ is increasing, φ|(−∞,0] = 0, φ|[1,∞) = 1}, C = {φ: R → R∣ φ is continuous, φ|(−∞,0] = 0, φ|[1,∞) = 1}. We prove that the above equation has at most one solution in C and that for some parameters α, β and p such a solution exists, and for some it does not. We also determine all solutions of the equation in Z and we show the exact connection between solutions in both classes.

Słowa kluczowe

EN

functional equations; increasing solutions; continuous distribution functions

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2005
• Tom: Vol. 53, no 4
• Strony: 389--399
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Morawiec J.

• Institute of Mathematics, Silesian University, Bankowa 14, PL-40-007 Katowice, Poland

autor

Reich L.

• Institut für Mathematik, Karl Franzens Universität, Heinrichstrasse 36, A-8010 Graz, Austria

Bibliografia

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