{"title":"毕达哥拉斯方法的应用和不同的从属关系","authors":"S. S. Kumar, Priyanka Goel","doi":"10.36045/j.bbms.210605","DOIUrl":null,"url":null,"abstract":"For $0\\leq\\alpha\\leq 1,$ let $H_{\\alpha}(x,y)$ be the convex weighted harmonic mean of $x$ and $y.$ We establish differential subordination implications of the form \\begin{equation*} H_{\\alpha}(p(z),p(z)\\Theta(z)+zp'(z)\\Phi(z))\\prec h(z)\\Rightarrow p(z)\\prec h(z), \\end{equation*} where $\\Phi,\\;\\Theta$ are analytic functions and $h$ is a univalent function satisfying some special properties. Further, we prove differential subordination implications involving a combination of three classical means. As an application, we generalize many existing results and obtain sufficient conditions for starlikeness and univalence.","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":"33 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2022-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Application of Pythagorean means and Differential Subordination\",\"authors\":\"S. S. Kumar, Priyanka Goel\",\"doi\":\"10.36045/j.bbms.210605\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For $0\\\\leq\\\\alpha\\\\leq 1,$ let $H_{\\\\alpha}(x,y)$ be the convex weighted harmonic mean of $x$ and $y.$ We establish differential subordination implications of the form \\\\begin{equation*} H_{\\\\alpha}(p(z),p(z)\\\\Theta(z)+zp'(z)\\\\Phi(z))\\\\prec h(z)\\\\Rightarrow p(z)\\\\prec h(z), \\\\end{equation*} where $\\\\Phi,\\\\;\\\\Theta$ are analytic functions and $h$ is a univalent function satisfying some special properties. Further, we prove differential subordination implications involving a combination of three classical means. As an application, we generalize many existing results and obtain sufficient conditions for starlikeness and univalence.\",\"PeriodicalId\":55309,\"journal\":{\"name\":\"Bulletin of the Belgian Mathematical Society-Simon Stevin\",\"volume\":\"33 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2022-03-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the Belgian Mathematical Society-Simon Stevin\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.36045/j.bbms.210605\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Belgian Mathematical Society-Simon Stevin","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.36045/j.bbms.210605","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Application of Pythagorean means and Differential Subordination
For $0\leq\alpha\leq 1,$ let $H_{\alpha}(x,y)$ be the convex weighted harmonic mean of $x$ and $y.$ We establish differential subordination implications of the form \begin{equation*} H_{\alpha}(p(z),p(z)\Theta(z)+zp'(z)\Phi(z))\prec h(z)\Rightarrow p(z)\prec h(z), \end{equation*} where $\Phi,\;\Theta$ are analytic functions and $h$ is a univalent function satisfying some special properties. Further, we prove differential subordination implications involving a combination of three classical means. As an application, we generalize many existing results and obtain sufficient conditions for starlikeness and univalence.
期刊介绍:
The Bulletin of the Belgian Mathematical Society - Simon Stevin (BBMS) is a peer-reviewed journal devoted to recent developments in all areas in pure and applied mathematics. It is published as one yearly volume, containing five issues.
The main focus lies on high level original research papers. They should aim to a broader mathematical audience in the sense that a well-written introduction is attractive to mathematicians outside the circle of experts in the subject, bringing motivation, background information, history and philosophy. The content has to be substantial enough: short one-small-result papers will not be taken into account in general, unless there are some particular arguments motivating publication, like an original point of view, a new short proof of a famous result etc.
The BBMS also publishes expository papers that bring the state of the art of a current mainstream topic in mathematics. Here it is even more important that at leat a substantial part of the paper is accessible to a broader audience of mathematicians.
The BBMS publishes papers in English, Dutch, French and German. All papers should have an abstract in English.