{"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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11253-024-02311-0","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We find all nonnegative solutions f of the equation
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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