Upper Bound of the Third Hankel Determinant for a Subclass of Close-to-Convex Functions Associated with the Lemniscate of Bernoulli
In this paper, our aim is to define a new subclass of close-to-convex functions in the open unit disk <inline-formula> <math display="inline"> <semantics> <mi mathvariant="double-struck">U</mi> </semantics> </math> </inline-formula>...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/7/9/848 |
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| author | Hari M. Srivastava Qazi Zahoor Ahmad Maslina Darus Nazar Khan Bilal Khan Naveed Zaman Hasrat Hussain Shah |
| author_facet | Hari M. Srivastava Qazi Zahoor Ahmad Maslina Darus Nazar Khan Bilal Khan Naveed Zaman Hasrat Hussain Shah |
| author_sort | Hari M. Srivastava |
| collection | DOAJ |
| description | In this paper, our aim is to define a new subclass of close-to-convex functions in the open unit disk <inline-formula> <math display="inline"> <semantics> <mi mathvariant="double-struck">U</mi> </semantics> </math> </inline-formula> that are related with the right half of the lemniscate of Bernoulli. For this function class, we obtain the upper bound of the third Hankel determinant. Various other related results are also considered. |
| first_indexed | 2024-04-13T16:01:52Z |
| format | Article |
| id | doaj.art-575ce335e87342f5a65f35f21230b482 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-04-13T16:01:52Z |
| publishDate | 2019-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-575ce335e87342f5a65f35f21230b4822022-12-22T02:40:30ZengMDPI AGMathematics2227-73902019-09-017984810.3390/math7090848math7090848Upper Bound of the Third Hankel Determinant for a Subclass of Close-to-Convex Functions Associated with the Lemniscate of BernoulliHari M. Srivastava0Qazi Zahoor Ahmad1Maslina Darus2Nazar Khan3Bilal Khan4Naveed Zaman5Hasrat Hussain Shah6Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, CanadaDepartment of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22010, PakistanSchool of Mathematical Sciences, Faculty of Sciences and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor, MalaysiaDepartment of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22010, PakistanDepartment of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22010, PakistanDepartment of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22010, PakistanDepartment of Mathematical Sciecnes, Balochistan University of Information Technology, Engineering and Management Sciences, Quetta 87300, PakistanIn this paper, our aim is to define a new subclass of close-to-convex functions in the open unit disk <inline-formula> <math display="inline"> <semantics> <mi mathvariant="double-struck">U</mi> </semantics> </math> </inline-formula> that are related with the right half of the lemniscate of Bernoulli. For this function class, we obtain the upper bound of the third Hankel determinant. Various other related results are also considered.https://www.mdpi.com/2227-7390/7/9/848analytic functionsclose-to-convex functionssubordinationlemniscate of Bernoulli Hankel determinant |
| spellingShingle | Hari M. Srivastava Qazi Zahoor Ahmad Maslina Darus Nazar Khan Bilal Khan Naveed Zaman Hasrat Hussain Shah Upper Bound of the Third Hankel Determinant for a Subclass of Close-to-Convex Functions Associated with the Lemniscate of Bernoulli Mathematics analytic functions close-to-convex functions subordination lemniscate of Bernoulli Hankel determinant |
| title | Upper Bound of the Third Hankel Determinant for a Subclass of Close-to-Convex Functions Associated with the Lemniscate of Bernoulli |
| title_full | Upper Bound of the Third Hankel Determinant for a Subclass of Close-to-Convex Functions Associated with the Lemniscate of Bernoulli |
| title_fullStr | Upper Bound of the Third Hankel Determinant for a Subclass of Close-to-Convex Functions Associated with the Lemniscate of Bernoulli |
| title_full_unstemmed | Upper Bound of the Third Hankel Determinant for a Subclass of Close-to-Convex Functions Associated with the Lemniscate of Bernoulli |
| title_short | Upper Bound of the Third Hankel Determinant for a Subclass of Close-to-Convex Functions Associated with the Lemniscate of Bernoulli |
| title_sort | upper bound of the third hankel determinant for a subclass of close to convex functions associated with the lemniscate of bernoulli |
| topic | analytic functions close-to-convex functions subordination lemniscate of Bernoulli Hankel determinant |
| url | https://www.mdpi.com/2227-7390/7/9/848 |
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