The Hankel determinant $H_{ 2,1}(F_{ f}/2)$ is defined as: \begin{ align*} H_{ 2,1}(F_{ f}/2):= \begin{ vmatrix} \gamma_1 & \gamma_2 \gamma_2 & \gamma_3 \end{ vmatrix}, \end{ align*} where $\gamma_1, \gamma_2,$ and $\gamma_3$ are the first, second and third logarithmic coefficients of functions belonging to the class $\mathcal{ S}$ of normalized univalent functions. In this article, we establish sharp inequalities $|H_{ 2,1}(F_{ f}/2)|\leq 1/16$ and $|H_{ 2,1}(F_{ f}/2)| \leq 23/3264$ for the logarithmic coefficients of starlike and convex functions associated with lune.
Categories: math.CV