B. Ráth, D. V. Krishna, K. S. Kumar, G. K. S. Viswanadh
{"title":"The sharp bound of the third Hankel determinants for inverse of starlike functions with respect to symmetric points","authors":"B. Ráth, D. V. Krishna, K. S. Kumar, G. K. S. Viswanadh","doi":"10.30970/ms.58.1.45-50","DOIUrl":null,"url":null,"abstract":"We study the sharp bound for the third Hankel determinant for the inverse function $f$, when it belongs to of the class of starlike functions with respect to symmetric points.Let $\\mathcal{S}^{\\ast}_{s}$ be the class of starlike functions with respect to symmetric points. In the article proves the following statements (Theorem): If $f\\in \\mathcal{S}^{\\ast}_{s}$ then\\begin{equation*}\\big|H_{3,1}(f^{-1})\\big|\\leq1,\\end{equation*}and the result is sharp for $f(z)=z/(1-z^2).$","PeriodicalId":37555,"journal":{"name":"Matematychni Studii","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Matematychni Studii","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.30970/ms.58.1.45-50","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 3
Abstract
We study the sharp bound for the third Hankel determinant for the inverse function $f$, when it belongs to of the class of starlike functions with respect to symmetric points.Let $\mathcal{S}^{\ast}_{s}$ be the class of starlike functions with respect to symmetric points. In the article proves the following statements (Theorem): If $f\in \mathcal{S}^{\ast}_{s}$ then\begin{equation*}\big|H_{3,1}(f^{-1})\big|\leq1,\end{equation*}and the result is sharp for $f(z)=z/(1-z^2).$