{"title":"Pre-Schwarzian and Schwarzian norm estimates for subclasses of univalent functions","authors":"Xiaoyuan Wang, Huijie Li, Jinhua Fan","doi":"10.1007/s00605-024-01971-1","DOIUrl":null,"url":null,"abstract":"<p>In the present article, we are focused to study the sharp estimates of the pre-Schwarzian and Schwarzian norms for subclasses of univalent functions. We will generalize the results of Carrasco and Hernández (Anal Math Phys 13(2):22, 2023) to the case of Janowski convex mappings in terms of the value <span>\\(h^{\\prime \\prime }(0)\\)</span>. We will also derive the sharp bound of pre-Schwarzian norm for a subclass of harmonic mappings whose fixed analytic part is a convex function of order <span>\\(\\alpha (0 \\le \\alpha <1)\\)</span>.</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Monatshefte für Mathematik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00605-024-01971-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
In the present article, we are focused to study the sharp estimates of the pre-Schwarzian and Schwarzian norms for subclasses of univalent functions. We will generalize the results of Carrasco and Hernández (Anal Math Phys 13(2):22, 2023) to the case of Janowski convex mappings in terms of the value \(h^{\prime \prime }(0)\). We will also derive the sharp bound of pre-Schwarzian norm for a subclass of harmonic mappings whose fixed analytic part is a convex function of order \(\alpha (0 \le \alpha <1)\).
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