{"title":"Sufficient and Necessary Conditions for the Generalized Distribution Series to be in Subclasses of Univalent Functions","authors":"","doi":"10.1007/s11253-024-02277-z","DOIUrl":null,"url":null,"abstract":"<p>We establish a relationship between the subclasses of univalent functions and generalized distribution series. The main aim of our investigation is to obtain necessary and sufficient conditions for the generalized distribution series to belong to the classes 𝒯 ℱ(ρ<em>,</em> ϑ)<em>,</em> 𝒯 ℋ(ρ<em>,</em> ϑ)<em>,</em> 𝒯 𝒥(ρ<em>,</em> ϑ)<em>,</em> and 𝒯 𝒳(ρ<em>,</em> ϑ) . In addition, we obtain some particular cases of our main results.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-06","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/s11253-024-02277-z","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 establish a relationship between the subclasses of univalent functions and generalized distribution series. The main aim of our investigation is to obtain necessary and sufficient conditions for the generalized distribution series to belong to the classes 𝒯 ℱ(ρ, ϑ), 𝒯 ℋ(ρ, ϑ), 𝒯 𝒥(ρ, ϑ), and 𝒯 𝒳(ρ, ϑ) . In addition, we obtain some particular cases of our main results.
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