On a functional equation characterizing some probability distributions

Justyna Jarczyk; Witold Jarczyk

doi:10.3842/umzh.v76i1.7672

Justyna Jarczyk Institute of Mathematics, University of Zielona Góra, Poland
Witold Jarczyk Institute of Mathematics, University of Zielona Góra, Poland

DOI: https://doi.org/10.3842/umzh.v76i1.7672

Keywords: Functional Equation, Iteration, Characterizing Function

Abstract

UDC 517.9

We find all nonnegative solutions $f$ of the equation \[f(x)=\prod^n_{j=1}f\left( s_jx\right)^{p_j},\] defined in a one-sided vicinity of $0$ and having a prescribed asymptotic at $0.$ The main theorem extends a result obtained by J. A. Baker [Proc. Amer. Math. Soc., 121, 767–773 (1994)].

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