Priya G. Krishnan, Ravichandran Vaithiyanathan, Ponnaiah Saikrishnan
{"title":"与解析函数的某些比率和线性组合相关的半径问题","authors":"Priya G. Krishnan, Ravichandran Vaithiyanathan, Ponnaiah Saikrishnan","doi":"10.1515/ms-2024-0066","DOIUrl":null,"url":null,"abstract":"For normalized starlike functions <jats:italic>f</jats:italic> : 𝔻 → ℂ, we consider the analytic functions <jats:italic>g</jats:italic> : 𝔻 → ℂ defined by <jats:italic>g</jats:italic>(<jats:italic>z</jats:italic>) = (1 + <jats:italic>z</jats:italic>(<jats:italic>f</jats:italic>″(<jats:italic>z</jats:italic>))/<jats:italic>f</jats:italic>′(<jats:italic>z</jats:italic>))/(<jats:italic>zf</jats:italic>′(<jats:italic>z</jats:italic>)/<jats:italic>f</jats:italic>(<jats:italic>z</jats:italic>)) and <jats:italic>g</jats:italic>(<jats:italic>z</jats:italic>) = (1 − <jats:italic>α</jats:italic>)(<jats:italic>zf</jats:italic>′(<jats:italic>z</jats:italic>))/<jats:italic>f</jats:italic>(<jats:italic>z</jats:italic>) + <jats:italic>α</jats:italic>(1 + (<jats:italic>zf</jats:italic>″(<jats:italic>z</jats:italic>))/<jats:italic>f</jats:italic>′(<jats:italic>z</jats:italic>)), 0 ≤ <jats:italic>α</jats:italic> ≤ 1. We determine the largest radius <jats:italic>ρ</jats:italic> with 0 < <jats:italic>ρ</jats:italic> ≤ 1 such that <jats:italic>g</jats:italic>(<jats:italic>ρ z</jats:italic>) is subordinate to various functions with positive real part.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"35 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Radius problem associated with certain ratios and linear combinations of analytic functions\",\"authors\":\"Priya G. Krishnan, Ravichandran Vaithiyanathan, Ponnaiah Saikrishnan\",\"doi\":\"10.1515/ms-2024-0066\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For normalized starlike functions <jats:italic>f</jats:italic> : 𝔻 → ℂ, we consider the analytic functions <jats:italic>g</jats:italic> : 𝔻 → ℂ defined by <jats:italic>g</jats:italic>(<jats:italic>z</jats:italic>) = (1 + <jats:italic>z</jats:italic>(<jats:italic>f</jats:italic>″(<jats:italic>z</jats:italic>))/<jats:italic>f</jats:italic>′(<jats:italic>z</jats:italic>))/(<jats:italic>zf</jats:italic>′(<jats:italic>z</jats:italic>)/<jats:italic>f</jats:italic>(<jats:italic>z</jats:italic>)) and <jats:italic>g</jats:italic>(<jats:italic>z</jats:italic>) = (1 − <jats:italic>α</jats:italic>)(<jats:italic>zf</jats:italic>′(<jats:italic>z</jats:italic>))/<jats:italic>f</jats:italic>(<jats:italic>z</jats:italic>) + <jats:italic>α</jats:italic>(1 + (<jats:italic>zf</jats:italic>″(<jats:italic>z</jats:italic>))/<jats:italic>f</jats:italic>′(<jats:italic>z</jats:italic>)), 0 ≤ <jats:italic>α</jats:italic> ≤ 1. We determine the largest radius <jats:italic>ρ</jats:italic> with 0 < <jats:italic>ρ</jats:italic> ≤ 1 such that <jats:italic>g</jats:italic>(<jats:italic>ρ z</jats:italic>) is subordinate to various functions with positive real part.\",\"PeriodicalId\":18282,\"journal\":{\"name\":\"Mathematica Slovaca\",\"volume\":\"35 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-08-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematica Slovaca\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/ms-2024-0066\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematica Slovaca","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/ms-2024-0066","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Radius problem associated with certain ratios and linear combinations of analytic functions
For normalized starlike functions f : 𝔻 → ℂ, we consider the analytic functions g : 𝔻 → ℂ defined by g(z) = (1 + z(f″(z))/f′(z))/(zf′(z)/f(z)) and g(z) = (1 − α)(zf′(z))/f(z) + α(1 + (zf″(z))/f′(z)), 0 ≤ α ≤ 1. We determine the largest radius ρ with 0 < ρ ≤ 1 such that g(ρ z) is subordinate to various functions with positive real part.
期刊介绍：
Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process. Its reputation was approved by many outstanding mathematicians who already contributed to Math. Slovaca. It makes bridges among mathematics, physics, soft computing, cryptography, biology, economy, measuring, etc. The Journal publishes original articles with complete proofs. Besides short notes the journal publishes also surveys as well as some issues are focusing on a theme of current interest.
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