A study of sharp coefficient bounds for a new subfamily of starlike functions

In this article, by employing the hyperbolic tangent function tanh z , a subfamily S tanh ∗ of starlike functions in the open unit disk D ⊂ C : D = { z : z ∈ C  and  | z | < 1 } is introduced and investigated. The main contribution of this article includes derivations of sharp inequalities involv...

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Bibliographic Details
Published in:Journal of inequalities and applications Vol. 2021; no. 1; pp. 1 - 20
Main Authors: Ullah, Khalil, Srivastava, H. M., Rafiq, Ayesha, Arif, Muhammad, Arjika, Sama
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 17.12.2021
Springer Nature B.V
SpringerOpen
Subjects:
Analysis
Analytic (or regular or holomorphic) functions
Applications of Mathematics
Coefficients
Estimates
Hyperbolic and trigonometric functions
Hyperbolic functions
Mathematics
Mathematics and Statistics
Principle of subordination
Schwarz function
Starlike functions
Univalent functions
Starlike functions
Analytic (or regular or holomorphic) functions
Schwarz function
Univalent functions
Fekete–Szegö functional
Coefficient bounds
The quantum or basic (or
calculus and its trivial
Principle of subordination
Hyperbolic and trigonometric functions
variation
ISSN:1029-242X, 1025-5834, 1029-242X
Online Access:Get full text
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Summary:In this article, by employing the hyperbolic tangent function tanh z , a subfamily S tanh ∗ of starlike functions in the open unit disk D ⊂ C : D = { z : z ∈ C  and  | z | < 1 } 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 ∗ of starlike functions in 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.
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content type line 14
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-021-02729-1