{"title":"单值函数子类的前施瓦兹和施瓦兹规范估计值","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":"64 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":\"64 1\",\"pages\":\"\"},\"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}","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}
Pre-Schwarzian and Schwarzian norm estimates for subclasses of univalent functions
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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