{"title":"论表征某些概率分布的函数方程","authors":"Justyna Jarczyk, Witold Jarczyk","doi":"10.1007/s11253-024-02311-0","DOIUrl":null,"url":null,"abstract":"<p>We find all nonnegative solutions <i>f</i> of the equation\n</p><span>$$f\\left(x\\right)=\\prod_{j=1}^{n}f{\\left({s}_{j}x\\right)}^{{p}_{j}},$$</span><p>defined in a one-sided vicinity of 0 and having a prescribed asymptotic at 0<i>.</i> The main theorem extends a result obtained by J. A. Baker [<i>Proc. Amer. Math. Soc.</i>, <b>121</b>, 767 (1994)].</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":"96 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On a Functional Equation Characterizing Some Probability Distributions\",\"authors\":\"Justyna Jarczyk, Witold Jarczyk\",\"doi\":\"10.1007/s11253-024-02311-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We find all nonnegative solutions <i>f</i> of the equation\\n</p><span>$$f\\\\left(x\\\\right)=\\\\prod_{j=1}^{n}f{\\\\left({s}_{j}x\\\\right)}^{{p}_{j}},$$</span><p>defined in a one-sided vicinity of 0 and having a prescribed asymptotic at 0<i>.</i> The main theorem extends a result obtained by J. A. Baker [<i>Proc. Amer. Math. Soc.</i>, <b>121</b>, 767 (1994)].</p>\",\"PeriodicalId\":49406,\"journal\":{\"name\":\"Ukrainian Mathematical Journal\",\"volume\":\"96 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-07-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ukrainian Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11253-024-02311-0\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ukrainian Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11253-024-02311-0","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
我们发现方程$$f\left(x\right)=\prod_{j=1}^{n}f{\left({s}_{j}x\right)}^{{p}_{j}}的所有非负解 f，$$定义在 0 的单边附近，并且在 0 处有规定的渐近线。 主定理扩展了 J. A. Baker [Proc. Amer. Math. Soc., 121, 767 (1994)] 所得到的结果。
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)].
期刊介绍：
Ukrainian Mathematical Journal publishes articles and brief communications on various areas of pure and applied mathematics and contains sections devoted to scientific information, bibliography, and reviews of current problems. It features contributions from researchers from the Ukrainian Mathematics Institute, the major scientific centers of the Ukraine and other countries.
Ukrainian Mathematical Journal is a translation of the peer-reviewed journal Ukrains’kyi Matematychnyi Zhurnal, a publication of the Institute of Mathematics of the National Academy of Sciences of Ukraine.
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