On a functional equation characterizing some probability distributions

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&a...

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Date:2024
Main Authors: Jarczyk, Justyna, Jarczyk, Witold
Format: Article
Language:English
Published: Institute of Mathematics, NAS of Ukraine 2024
Online Access:https://umj.imath.kiev.ua/index.php/umj/article/view/7672
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Journal Title:Ukrains’kyi Matematychnyi Zhurnal

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Ukrains’kyi Matematychnyi Zhurnal
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author Jarczyk, Justyna
Jarczyk, Witold
Jarczyk, Justyna
Jarczyk, Witold
author_facet Jarczyk, Justyna
Jarczyk, Witold
Jarczyk, Justyna
Jarczyk, Witold
author_institution_txt_mv [ { "author": "Justyna Jarczyk", "institution": "Institute of Mathematics, University of Zielona Góra, Poland" }, { "author": "Witold Jarczyk", "institution": "Institute of Mathematics, University of Zielona Góra, Poland" } ]
author_sort Jarczyk, Justyna
baseUrl_str https://umj.imath.kiev.ua/index.php/umj/oai
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datestamp_date 2024-06-19T00:35:07Z
description 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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spelling umjimathkievua-article-76722024-06-19T00:35:07Z On a functional equation characterizing some probability distributions On a functional equation characterizing some probability distributions Jarczyk, Justyna Jarczyk, Witold Jarczyk, Justyna Jarczyk, Witold Functional Equation Iteration Characterizing Function Mathematical Analysis Iterative Functional Equations 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)]. УДК 517.9 Про функціональне рівняння, що характеризує деякі ймовірнісні розподіли  Знайдено всі невід’ємні розв’язки $f$ рівняння \[f(x)=\prod^n_{j=1}f\left( s_jx\right)^{p_j},\] що визначені в односторонньому околі $0$ і мають задану асимптотику в $0.$  Основна теорема розширює результат Дж. А. Бейкерa [Proc. Amer. Math. Soc., 121, 767–773  (1994)]. Institute of Mathematics, NAS of Ukraine 2024-02-02 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/7672 10.3842/umzh.v76i1.7672 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 1 (2024); 107 - 114 Український математичний журнал; Том 76 № 1 (2024); 107 - 114 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7672/9682 Copyright (c) 2024 Witold Jarczyk
spellingShingle Jarczyk, Justyna
Jarczyk, Witold
Jarczyk, Justyna
Jarczyk, Witold
On a functional equation characterizing some probability distributions
title On a functional equation characterizing some probability distributions
title_alt On a functional equation characterizing some probability distributions
title_full On a functional equation characterizing some probability distributions
title_fullStr On a functional equation characterizing some probability distributions
title_full_unstemmed On a functional equation characterizing some probability distributions
title_short On a functional equation characterizing some probability distributions
title_sort on a functional equation characterizing some probability distributions
topic_facet Functional Equation
Iteration
Characterizing Function
Mathematical Analysis
Iterative Functional Equations
url https://umj.imath.kiev.ua/index.php/umj/article/view/7672
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