An Upper Bound of the Third Hankel Determinant for a Subclass of <i>q</i>-Starlike Functions Associated with <i>k</i>-Fibonacci Numbers
In this paper, we use <i>q</i>-derivative operator to define a new class of <i>q</i>-starlike functions associated with <i>k</i>-Fibonacci numbers. This newly defined class is a subclass of class <inline-formula> <math display="inline"> <s...
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| Format: | Article |
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MDPI AG
2020-06-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/6/1043 |
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| author | Muhammad Shafiq Hari M. Srivastava Nazar Khan Qazi Zahoor Ahmad Maslina Darus Samiha Kiran |
| author_facet | Muhammad Shafiq Hari M. Srivastava Nazar Khan Qazi Zahoor Ahmad Maslina Darus Samiha Kiran |
| author_sort | Muhammad Shafiq |
| collection | DOAJ |
| description | In this paper, we use <i>q</i>-derivative operator to define a new class of <i>q</i>-starlike functions associated with <i>k</i>-Fibonacci numbers. This newly defined class is a subclass of class <inline-formula> <math display="inline"> <semantics> <mi mathvariant="script">A</mi> </semantics> </math> </inline-formula> of normalized analytic functions, where class <inline-formula> <math display="inline"> <semantics> <mi mathvariant="script">A</mi> </semantics> </math> </inline-formula> is invariant (or symmetric) under rotations. For this function class we obtain an upper bound of the third Hankel determinant. |
| first_indexed | 2024-03-10T18:57:41Z |
| format | Article |
| id | doaj.art-cacc48cc3dc14104897bd2abacb4cd08 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T18:57:41Z |
| publishDate | 2020-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-cacc48cc3dc14104897bd2abacb4cd082023-11-20T04:37:43ZengMDPI AGSymmetry2073-89942020-06-01126104310.3390/sym12061043An Upper Bound of the Third Hankel Determinant for a Subclass of <i>q</i>-Starlike Functions Associated with <i>k</i>-Fibonacci NumbersMuhammad Shafiq0Hari M. Srivastava1Nazar Khan2Qazi Zahoor Ahmad3Maslina Darus4Samiha Kiran5Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22010, PakistanDepartment of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, CanadaDepartment of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22010, PakistanGovernment Akhtar Nawaz Khan (Shaheed) Degree College KTS, Haripur 22620, PakistanDepartment of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor, MalaysiaDepartment of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22010, PakistanIn this paper, we use <i>q</i>-derivative operator to define a new class of <i>q</i>-starlike functions associated with <i>k</i>-Fibonacci numbers. This newly defined class is a subclass of class <inline-formula> <math display="inline"> <semantics> <mi mathvariant="script">A</mi> </semantics> </math> </inline-formula> of normalized analytic functions, where class <inline-formula> <math display="inline"> <semantics> <mi mathvariant="script">A</mi> </semantics> </math> </inline-formula> is invariant (or symmetric) under rotations. For this function class we obtain an upper bound of the third Hankel determinant.https://www.mdpi.com/2073-8994/12/6/1043starlike functionssubordination<i>q</i>-Differential operator<i>k</i>-Fibonacci numbers |
| spellingShingle | Muhammad Shafiq Hari M. Srivastava Nazar Khan Qazi Zahoor Ahmad Maslina Darus Samiha Kiran An Upper Bound of the Third Hankel Determinant for a Subclass of <i>q</i>-Starlike Functions Associated with <i>k</i>-Fibonacci Numbers Symmetry starlike functions subordination <i>q</i>-Differential operator <i>k</i>-Fibonacci numbers |
| title | An Upper Bound of the Third Hankel Determinant for a Subclass of <i>q</i>-Starlike Functions Associated with <i>k</i>-Fibonacci Numbers |
| title_full | An Upper Bound of the Third Hankel Determinant for a Subclass of <i>q</i>-Starlike Functions Associated with <i>k</i>-Fibonacci Numbers |
| title_fullStr | An Upper Bound of the Third Hankel Determinant for a Subclass of <i>q</i>-Starlike Functions Associated with <i>k</i>-Fibonacci Numbers |
| title_full_unstemmed | An Upper Bound of the Third Hankel Determinant for a Subclass of <i>q</i>-Starlike Functions Associated with <i>k</i>-Fibonacci Numbers |
| title_short | An Upper Bound of the Third Hankel Determinant for a Subclass of <i>q</i>-Starlike Functions Associated with <i>k</i>-Fibonacci Numbers |
| title_sort | upper bound of the third hankel determinant for a subclass of i q i starlike functions associated with i k i fibonacci numbers |
| topic | starlike functions subordination <i>q</i>-Differential operator <i>k</i>-Fibonacci numbers |
| url | https://www.mdpi.com/2073-8994/12/6/1043 |
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