Sharp Coefficient Bounds for Starlike Functions Associated with Cosine Function

Let S_^ denote the class of normalized analytic functions f in the open unit disk D satisfying the subordination zf^ (z) f (z) 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 S_^. The first result of the next section deals with the sharp upper bounds of the logarithmic coefficients ₃ and ₄ and we found in addition the sharp upper bound for |H₂, ₂ (F₅/2) |. 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.