Coefficient inequalities and Hankel determinant for a new subclass of q-starlike functions
Abstract In this study, for 0 < q < 1 $0< q<1$ , we first introduce a function φ q ( τ ) = e q τ − 1 q ( 1 − q τ ) $\varphi _{q}\left ( \tau \right ) = \frac{e^{q\tau }-1}{q\left ( 1-q\tau \right ) }$ and prove that φ q ( τ ) $\varphi _{q}\left ( \tau \right ) $ is convex univalent in th...
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| Format: | Article |
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SpringerOpen
2025-08-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | https://doi.org/10.1186/s13660-025-03337-z |
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| author | Mohammad Faisal Khan Mohammed Abaoud |
| author_facet | Mohammad Faisal Khan Mohammed Abaoud |
| author_sort | Mohammad Faisal Khan |
| collection | DOAJ |
| description | Abstract In this study, for 0 < q < 1 $0< q<1$ , we first introduce a function φ q ( τ ) = e q τ − 1 q ( 1 − q τ ) $\varphi _{q}\left ( \tau \right ) = \frac{e^{q\tau }-1}{q\left ( 1-q\tau \right ) }$ and prove that φ q ( τ ) $\varphi _{q}\left ( \tau \right ) $ is convex univalent in the open unit disk U $\mathcal{U}$ for all q ∈ ( 0 , 0.32 ) $q\in \left ( 0,0.32\right ) $ . Further, using the subordination technique and considering q-difference operator, we define a new subclass S φ ∗ ( q ) $S_{\varphi }^{\ast }(q)$ of q-starlike functions associated with a function 1 + φ q ( τ ) $1+\varphi _{q}\left ( \tau \right ) $ , which is in the class P $\mathcal{P}$ . Some new geometric properties, such as coefficient bounds, Feketo–Szego inequalities, and the upper bound of the second-order Hankel determinant, are investigated for the function h belonging to the class S φ ∗ ( q ) $S_{\varphi }^{\ast }(q)$ . |
| format | Article |
| id | doaj-art-78f41fda9543458593bf391d959e90b6 |
| institution | Kabale University |
| issn | 1029-242X |
| language | English |
| publishDate | 2025-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj-art-78f41fda9543458593bf391d959e90b62025-08-20T04:02:41ZengSpringerOpenJournal of Inequalities and Applications1029-242X2025-08-012025111310.1186/s13660-025-03337-zCoefficient inequalities and Hankel determinant for a new subclass of q-starlike functionsMohammad Faisal Khan0Mohammed Abaoud1Department of Basic Sciences, College of Science, and Theoretical Studies, Saudi Electronic UniversityDepartment of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU)Abstract In this study, for 0 < q < 1 $0< q<1$ , we first introduce a function φ q ( τ ) = e q τ − 1 q ( 1 − q τ ) $\varphi _{q}\left ( \tau \right ) = \frac{e^{q\tau }-1}{q\left ( 1-q\tau \right ) }$ and prove that φ q ( τ ) $\varphi _{q}\left ( \tau \right ) $ is convex univalent in the open unit disk U $\mathcal{U}$ for all q ∈ ( 0 , 0.32 ) $q\in \left ( 0,0.32\right ) $ . Further, using the subordination technique and considering q-difference operator, we define a new subclass S φ ∗ ( q ) $S_{\varphi }^{\ast }(q)$ of q-starlike functions associated with a function 1 + φ q ( τ ) $1+\varphi _{q}\left ( \tau \right ) $ , which is in the class P $\mathcal{P}$ . Some new geometric properties, such as coefficient bounds, Feketo–Szego inequalities, and the upper bound of the second-order Hankel determinant, are investigated for the function h belonging to the class S φ ∗ ( q ) $S_{\varphi }^{\ast }(q)$ .https://doi.org/10.1186/s13660-025-03337-zAnalytic and univalent functionsHankel determinantq-Starlike functionsSubordination |
| spellingShingle | Mohammad Faisal Khan Mohammed Abaoud Coefficient inequalities and Hankel determinant for a new subclass of q-starlike functions Journal of Inequalities and Applications Analytic and univalent functions Hankel determinant q-Starlike functions Subordination |
| title | Coefficient inequalities and Hankel determinant for a new subclass of q-starlike functions |
| title_full | Coefficient inequalities and Hankel determinant for a new subclass of q-starlike functions |
| title_fullStr | Coefficient inequalities and Hankel determinant for a new subclass of q-starlike functions |
| title_full_unstemmed | Coefficient inequalities and Hankel determinant for a new subclass of q-starlike functions |
| title_short | Coefficient inequalities and Hankel determinant for a new subclass of q-starlike functions |
| title_sort | coefficient inequalities and hankel determinant for a new subclass of q starlike functions |
| topic | Analytic and univalent functions Hankel determinant q-Starlike functions Subordination |
| url | https://doi.org/10.1186/s13660-025-03337-z |
| work_keys_str_mv | AT mohammadfaisalkhan coefficientinequalitiesandhankeldeterminantforanewsubclassofqstarlikefunctions AT mohammedabaoud coefficientinequalitiesandhankeldeterminantforanewsubclassofqstarlikefunctions |