Sharp Coefficient Bounds for Starlike Functions Associated with Cosine Function

Let Scos^ denote the class of normalized analytic functions f in the open unit disk D satisfying the subordination zf^(z)f(z)cos z. In the second section of this article we find the sharp upper bounds for the initial coefficients a₃, a₄ and a₅ and the sharp upper bound for module of the Hankel determinant |H2,3(f)| for the functions from the class Scos^. The first result of the next section deals with the sharp upper bounds of the logarithmic coefficients γ₃ and γ₄ and we found in addition the sharp upper bound for |H2,2(Ff/2)|. 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{} 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].