A study of sharp coefficient bounds for a new subfamily of starlike functions
Abstract In this article, by employing the hyperbolic tangent function tanhz, a subfamily S tanh ∗ $\mathcal{S}_{\tanh }^{\ast }$ of starlike functions in the open unit disk D ⊂ C $\mathbb{D}\subset \mathbb{C}$ : D = { z : z ∈ C and | z | < 1 } $$\begin{aligned} \mathbb{D}= \bigl\{ z:z\in \math...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-12-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-021-02729-1 |
| _version_ | 1831717551447474176 |
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| author | Khalil Ullah H. M. Srivastava Ayesha Rafiq Muhammad Arif Sama Arjika |
| author_facet | Khalil Ullah H. M. Srivastava Ayesha Rafiq Muhammad Arif Sama Arjika |
| author_sort | Khalil Ullah |
| collection | DOAJ |
| description | Abstract In this article, by employing the hyperbolic tangent function tanhz, a subfamily S tanh ∗ $\mathcal{S}_{\tanh }^{\ast }$ of starlike functions in the open unit disk D ⊂ C $\mathbb{D}\subset \mathbb{C}$ : D = { z : z ∈ C and | z | < 1 } $$\begin{aligned} \mathbb{D}= \bigl\{ z:z\in \mathbb{C} \text{ and } \vert z \vert < 1 \bigr\} \end{aligned}$$ is introduced and investigated. The main contribution of this article includes derivations of sharp inequalities involving the Taylor–Maclaurin coefficients for functions belonging to the class S tanh ∗ $\mathcal{S}_{\tanh }^{\ast } $ of starlike functions in D $\mathbb{D}$ . In particular, the bounds of the first three Taylor–Maclaurin coefficients, the estimates of the Fekete–Szegö type functionals, and the estimates of the second- and third-order Hankel determinants are the main problems that are proposed to be studied here. |
| first_indexed | 2024-12-21T01:01:21Z |
| format | Article |
| id | doaj.art-ab29febb3eab441595018350d366da63 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-21T01:01:21Z |
| publishDate | 2021-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-ab29febb3eab441595018350d366da632022-12-21T19:21:10ZengSpringerOpenJournal of Inequalities and Applications1029-242X2021-12-012021112010.1186/s13660-021-02729-1A study of sharp coefficient bounds for a new subfamily of starlike functionsKhalil Ullah0H. M. Srivastava1Ayesha Rafiq2Muhammad Arif3Sama Arjika4Department of Mathematics, Abdul Wali khan UniversityDepartment of Mathematics and Statistics, University of VictoriaInstitute of Space Technology, University of IslamabadDepartment of Mathematics, Abdul Wali khan UniversityDepartment of Mathematics and Informatics, University of AgadezAbstract In this article, by employing the hyperbolic tangent function tanhz, a subfamily S tanh ∗ $\mathcal{S}_{\tanh }^{\ast }$ of starlike functions in the open unit disk D ⊂ C $\mathbb{D}\subset \mathbb{C}$ : D = { z : z ∈ C and | z | < 1 } $$\begin{aligned} \mathbb{D}= \bigl\{ z:z\in \mathbb{C} \text{ and } \vert z \vert < 1 \bigr\} \end{aligned}$$ is introduced and investigated. The main contribution of this article includes derivations of sharp inequalities involving the Taylor–Maclaurin coefficients for functions belonging to the class S tanh ∗ $\mathcal{S}_{\tanh }^{\ast } $ of starlike functions in D $\mathbb{D}$ . In particular, the bounds of the first three Taylor–Maclaurin coefficients, the estimates of the Fekete–Szegö type functionals, and the estimates of the second- and third-order Hankel determinants are the main problems that are proposed to be studied here.https://doi.org/10.1186/s13660-021-02729-1Analytic (or regular or holomorphic) functionsUnivalent functionsStarlike functionsPrinciple of subordinationSchwarz functionHyperbolic and trigonometric functions |
| spellingShingle | Khalil Ullah H. M. Srivastava Ayesha Rafiq Muhammad Arif Sama Arjika A study of sharp coefficient bounds for a new subfamily of starlike functions Journal of Inequalities and Applications Analytic (or regular or holomorphic) functions Univalent functions Starlike functions Principle of subordination Schwarz function Hyperbolic and trigonometric functions |
| title | A study of sharp coefficient bounds for a new subfamily of starlike functions |
| title_full | A study of sharp coefficient bounds for a new subfamily of starlike functions |
| title_fullStr | A study of sharp coefficient bounds for a new subfamily of starlike functions |
| title_full_unstemmed | A study of sharp coefficient bounds for a new subfamily of starlike functions |
| title_short | A study of sharp coefficient bounds for a new subfamily of starlike functions |
| title_sort | study of sharp coefficient bounds for a new subfamily of starlike functions |
| topic | Analytic (or regular or holomorphic) functions Univalent functions Starlike functions Principle of subordination Schwarz function Hyperbolic and trigonometric functions |
| url | https://doi.org/10.1186/s13660-021-02729-1 |
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