Some results for the family of univalent functions related with Limaçon domain
The investigation of univalent functions is one of the fundamental ideas of Geometric function theory (GFT). However, the class of these functions cannot be investigated as a whole for some particular kind of problems. As a result, the study of its subclasses has been receiving numerous attentions....
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| Language: | English |
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AIMS Press
2021-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | http://www.aimspress.com/article/doi/10.3934/math.2021204?viewType=HTML |
| _version_ | 1818331106380873728 |
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| author | Afis Saliu Khalida Inayat Noor Saqib Hussain Maslina Darus |
| author_facet | Afis Saliu Khalida Inayat Noor Saqib Hussain Maslina Darus |
| author_sort | Afis Saliu |
| collection | DOAJ |
| description | The investigation of univalent functions is one of the fundamental ideas of Geometric function theory (GFT). However, the class of these functions cannot be investigated as a whole for some particular kind of problems. As a result, the study of its subclasses has been receiving numerous attentions. In this direction, subfamilies of the class of univalent functions that map the open unit disc onto the domain bounded by limaçon of Pascal were recently introduced in the literature. Due to the several applications of this domain in Mathematics, Statistics (hypothesis testing problem) and Engineering (rotary fluid processing machines such as pumps, compressors, motors and engines.), continuous investigation of these classes are of interest in this article. To this end, the family of functions for which $ \frac{\varsigma f^{\prime}(\varsigma)}{f(\varsigma)} $ and $ \frac{(\varsigma f^{\prime}(\varsigma))^{\prime}}{f^{\prime}(\varsigma)} $ map open unit disc onto region bounded by limaçon are studied. Coefficients bounds, Fekete Szeg $ \ddot{ \rm{o}} $ inequalities and the bounds of the third Hankel determinants are derived. Furthermore, the sharp radius for which the classes are linked to each other and to the notable subclasses of univalent functions are found. Finally, the idea of subordination is utilized to obtain some results for functions belonging to these classes. |
| first_indexed | 2024-12-13T13:14:34Z |
| format | Article |
| id | doaj.art-e076245d26a0441d810c5a24ceeaac7a |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-13T13:14:34Z |
| publishDate | 2021-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-e076245d26a0441d810c5a24ceeaac7a2022-12-21T23:44:35ZengAIMS PressAIMS Mathematics2473-69882021-01-01643410343110.3934/math.2021204Some results for the family of univalent functions related with Limaçon domainAfis Saliu0Khalida Inayat Noor1Saqib Hussain2Maslina Darus31. Department of Mathematics, COMSATS University Islamabad, Park Road, Tarlai Kalan, Islamabad 45550, Pakistan1. Department of Mathematics, COMSATS University Islamabad, Park Road, Tarlai Kalan, Islamabad 45550, Pakistan2. Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus 22060, Pakistan3. Department of Mathematical Sciences, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor, MalaysiaThe investigation of univalent functions is one of the fundamental ideas of Geometric function theory (GFT). However, the class of these functions cannot be investigated as a whole for some particular kind of problems. As a result, the study of its subclasses has been receiving numerous attentions. In this direction, subfamilies of the class of univalent functions that map the open unit disc onto the domain bounded by limaçon of Pascal were recently introduced in the literature. Due to the several applications of this domain in Mathematics, Statistics (hypothesis testing problem) and Engineering (rotary fluid processing machines such as pumps, compressors, motors and engines.), continuous investigation of these classes are of interest in this article. To this end, the family of functions for which $ \frac{\varsigma f^{\prime}(\varsigma)}{f(\varsigma)} $ and $ \frac{(\varsigma f^{\prime}(\varsigma))^{\prime}}{f^{\prime}(\varsigma)} $ map open unit disc onto region bounded by limaçon are studied. Coefficients bounds, Fekete Szeg $ \ddot{ \rm{o}} $ inequalities and the bounds of the third Hankel determinants are derived. Furthermore, the sharp radius for which the classes are linked to each other and to the notable subclasses of univalent functions are found. Finally, the idea of subordination is utilized to obtain some results for functions belonging to these classes.http://www.aimspress.com/article/doi/10.3934/math.2021204?viewType=HTMLunivalent functionsschwarz functionslimaçon domainsubordinationhankel determinan |
| spellingShingle | Afis Saliu Khalida Inayat Noor Saqib Hussain Maslina Darus Some results for the family of univalent functions related with Limaçon domain AIMS Mathematics univalent functions schwarz functions limaçon domain subordination hankel determinan |
| title | Some results for the family of univalent functions related with Limaçon domain |
| title_full | Some results for the family of univalent functions related with Limaçon domain |
| title_fullStr | Some results for the family of univalent functions related with Limaçon domain |
| title_full_unstemmed | Some results for the family of univalent functions related with Limaçon domain |
| title_short | Some results for the family of univalent functions related with Limaçon domain |
| title_sort | some results for the family of univalent functions related with limacon domain |
| topic | univalent functions schwarz functions limaçon domain subordination hankel determinan |
| url | http://www.aimspress.com/article/doi/10.3934/math.2021204?viewType=HTML |
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