Analyzing Functions Mapping the Unit Disk to Limaçon Domain
This paper focuses on a particular type of starlike univalent function, namely $(1-sz)(1+z)$ with $-1/3\leq s\leq 1/3$. This function maps the open unit disk $\mathbb{D}$ onto a Limaçon domain denoted by \[ \left[(u-1)^2+v^2-s^2\right]^2<(1-s)^2\left[\left(u-1-s\right)^2+v^2\right].\] The prim...
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| Language: | English |
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University of Maragheh
2024-10-01
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| Series: | Sahand Communications in Mathematical Analysis |
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| Online Access: | https://scma.maragheh.ac.ir/article_716190_abcf4f3a42cfac7cd7de2b3add90ac68.pdf |
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| author | Vali Soltani Masih Shahram Najafzadeh |
| author_facet | Vali Soltani Masih Shahram Najafzadeh |
| author_sort | Vali Soltani Masih |
| collection | DOAJ |
| description | This paper focuses on a particular type of starlike univalent function, namely $(1-sz)(1+z)$ with $-1/3\leq s\leq 1/3$. This function maps the open unit disk $\mathbb{D}$ onto a Limaçon domain denoted by \[ \left[(u-1)^2+v^2-s^2\right]^2<(1-s)^2\left[\left(u-1-s\right)^2+v^2\right].\] The primary investigation concerns on analytic function families where $zh'/h$ maps the unit disk to a subset of this domain. The paper provides the lower and upper bounds of the real and imaginary parts of these functions and highlights some distinguishing characteristics of these bounds. Furthermore, the study employed subordination theory to derive conclusions and corollaries for functions belonging to the aforementioned class. |
| format | Article |
| id | doaj-art-fe21dc579a7a408bbf6dc73258e69b79 |
| institution | Kabale University |
| issn | 2322-5807 2423-3900 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj-art-fe21dc579a7a408bbf6dc73258e69b792025-02-11T05:27:48ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002024-10-0121422323910.22130/scma.2024.2016346.1542716190Analyzing Functions Mapping the Unit Disk to Limaçon DomainVali Soltani Masih0Shahram Najafzadeh1Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395-3697, Tehran, Iran.Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395-3697, Tehran, Iran.This paper focuses on a particular type of starlike univalent function, namely $(1-sz)(1+z)$ with $-1/3\leq s\leq 1/3$. This function maps the open unit disk $\mathbb{D}$ onto a Limaçon domain denoted by \[ \left[(u-1)^2+v^2-s^2\right]^2<(1-s)^2\left[\left(u-1-s\right)^2+v^2\right].\] The primary investigation concerns on analytic function families where $zh'/h$ maps the unit disk to a subset of this domain. The paper provides the lower and upper bounds of the real and imaginary parts of these functions and highlights some distinguishing characteristics of these bounds. Furthermore, the study employed subordination theory to derive conclusions and corollaries for functions belonging to the aforementioned class.https://scma.maragheh.ac.ir/article_716190_abcf4f3a42cfac7cd7de2b3add90ac68.pdfunivalent functionssubordinationstarlike functionsdomain bounded by limacon |
| spellingShingle | Vali Soltani Masih Shahram Najafzadeh Analyzing Functions Mapping the Unit Disk to Limaçon Domain Sahand Communications in Mathematical Analysis univalent functions subordination starlike functions domain bounded by limacon |
| title | Analyzing Functions Mapping the Unit Disk to Limaçon Domain |
| title_full | Analyzing Functions Mapping the Unit Disk to Limaçon Domain |
| title_fullStr | Analyzing Functions Mapping the Unit Disk to Limaçon Domain |
| title_full_unstemmed | Analyzing Functions Mapping the Unit Disk to Limaçon Domain |
| title_short | Analyzing Functions Mapping the Unit Disk to Limaçon Domain |
| title_sort | analyzing functions mapping the unit disk to limacon domain |
| topic | univalent functions subordination starlike functions domain bounded by limacon |
| url | https://scma.maragheh.ac.ir/article_716190_abcf4f3a42cfac7cd7de2b3add90ac68.pdf |
| work_keys_str_mv | AT valisoltanimasih analyzingfunctionsmappingtheunitdisktolimacondomain AT shahramnajafzadeh analyzingfunctionsmappingtheunitdisktolimacondomain |