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Sharp Coefficient Bounds for Starlike Functions Associated with Cosine Function
Version 1
: Received: 3 June 2024 / Approved: 3 June 2024 / Online: 4 June 2024 (02:28:17 CEST)
A peer-reviewed article of this Preprint also exists.
Ali, R.; Raza, M.; Bulboacă, T. Sharp Coefficient Bounds for Starlike Functions Associated with Cosine Function †. Axioms 2024, 13, 442. Ali, R.; Raza, M.; Bulboacă, T. Sharp Coefficient Bounds for Starlike Functions Associated with Cosine Function †. Axioms 2024, 13, 442.
Abstract
Let $\mathcal{\mathcal{S}}_{\cos}^{\ast}$ denote the class of normalized analytic functions $f$ in the open unit disk $\mathbb{D}$ satisfying the subordination $\dfrac{zf^{\prime}(z)}{f(z)}\prec\cos z$. In the second section of this article we find the sharp upper bounds for the initial coefficients $a_{3}$, $a_{4}$ and $a_{5}$ and the sharp upper bound for module of the Hankel determinant $|H_{2,3}(f)|$ for the functions from the class $\mathcal{S}_{\cos}^{\ast}$. The first result of the next section deals with the sharp upper bounds of the logarithmic coefficients $\gamma_{3}$ and $\gamma_{4}$ and we found in addition the sharp upper bound for $\left|H_{2,2}\left(F_{f}/2\right)\right|$. For obtaining these results we used the very useful and appropriate Lemma 2.4 of N.E. Cho et al. [Filomat 34(6) (2020), 2061--2072], and the technique for finding the maximum value of a three variable function on a closed cuboid. All the maximum found values were checked by using MAPLE\texttrademark{} computare software, and we also found the extremal functions in each cases. All of our present results are the best ones and give sharp versions of those recently published in [Hacet. J. Math. Stat. 52, 596--618, 2023].
Keywords
starlike functions; subordination; cosine functions; initial coefficient bounds; Hankel determinants; logarithmic coefficients
Subject
Computer Science and Mathematics, Analysis
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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