Certain Coefficient Problems of $\mathcal{S}_{e}^{*}$ and $\mathcal{C}_{e}$
S. Sivaprasad Kumar, Neha Verma
TL;DR
This paper derives sharp bounds for the third Hankel determinant and estimates for coefficients and higher-order determinants for functions in the classes and , advancing the understanding of their geometric properties.
Contribution
It provides new sharp bounds and coefficient estimates for functions in the classes and , including higher-order Hankel determinants.
Findings
Sharp bounds for the third Hankel determinant obtained.
Coefficient estimates for the sixth and seventh coefficients provided.
Fourth-order Hankel determinant established.
Abstract
In this current study, we consider the classes and to obtain sharp bounds for the third Hankel determinant for functions within these classes. Additionally, we provide estimates for the sixth and seventh coefficients while establishing the fourth-order Hankel determinant as well.
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Taxonomy
TopicsMathematical functions and polynomials · Analytic and geometric function theory