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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| Дата: | 2024 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2024
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512704958038016 |
|---|---|
| author | Jarczyk, Justyna Jarczyk, Witold Jarczyk, Justyna Jarczyk, Witold |
| author_facet | Jarczyk, Justyna Jarczyk, Witold Jarczyk, Justyna Jarczyk, Witold |
| author_sort | Jarczyk, Justyna |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| 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)]. |
| doi_str_mv | 10.3842/umzh.v76i1.7672 |
| first_indexed | 2026-03-24T03:33:01Z |
| format | Article |
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On a Functional Equation Characterizing Some Probability Distributions
Published: 30 July 2024
Volume 76, pages 112–121, (2024)
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Justyna Jarczyk1 &
Witold Jarczyk1
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We find all nonnegative solutions f of the equation
$$f\left(x\right)=\prod_{j=1}^{n}f{\left({s}_{j}x\right)}^{{p}_{j}},$$
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 (1994)].
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Institute of Mathematics, University of Zielona Góra, Zielona Góra, Poland
Justyna Jarczyk & Witold Jarczyk
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 76, No. 1, pp. 107–114, January, 2024. Ukrainian DOI: https://doi.org/10.3842/umzh.v76i1.7672.
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Jarczyk, J., Jarczyk, W. On a Functional Equation Characterizing Some Probability Distributions.
Ukr Math J 76, 112–121 (2024). https://doi.org/10.1007/s11253-024-02311-0
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Received: 10 July 2023
Published: 30 July 2024
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Issue date: June 2024
DOI: https://doi.org/10.1007/s11253-024-02311-0
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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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