The Fourth-order Hankel Determinant for Certain Subclasses of Star-like Functions Subordinate to Exponential Function

ZHANG Haiyan; TANG Huo; MA Lina

doi:10.6054/j.jscnun.2021062

Journal of South China Normal University (Natural Science Edition) > 2021 > 53(4): 84-90. > DOI: 10.6054/j.jscnun.2021062

ZHANG Haiyan, TANG Huo, MA Lina. The Fourth-order Hankel Determinant for Certain Subclasses of Star-like Functions Subordinate to Exponential Function[J]. Journal of South China Normal University (Natural Science Edition), 2021, 53(4): 84-90. DOI: 10.6054/j.jscnun.2021062

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The Fourth-order Hankel Determinant for Certain Subclasses of Star-like Functions Subordinate to Exponential Function

School of Mathematics and Computer Sciences, Chifeng University, Chifeng 024000, China

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Received Date: November 29, 2020
Available Online: September 02, 2021

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Abstract

Abstract

Let $\mathcal{A}$ be a family of analytic functions with are the form $f(z)=z+\sum\limits_{n=2}^{\infty} a_{n} z^{n}$ on the open unit disk D. A class of analytic functions S_e^* which are defined on the open unit cicle D and associated with exponential function is introduced, that is $S_{e}^{*}=\left\{f \mid \frac{z f^{\prime}(z)}{f(z)}\prec\mathrm{e}^{z} \quad(f \in \mathcal{A}, z \in D)\right\}.$ And the upper bound of the fourth-order Hankel determinant H₄(1) for this function class S_e^* associated with exponential function is given.
- analytic function,
- Hankel determinant,
- exponential function,
- upper bound

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The Fourth-order Hankel Determinant for Certain Subclasses of Star-like Functions Subordinate to Exponential Function

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