On the initial coefficient differences of Ma-Minda starlike functions and bounded turning functions

Source abstract

Let $\Phi$ be a univalent function in the unit disk $\mathbb{D}$ and let $\Phi (\mathbb{D})$ be symmetric with respect to the real axis and starlike with respect to $\Phi(0)=1$, also $\Phi ^{\prime }(0)>0$. For the given function $\Phi$, let $\mathcal{S^{\ast }}(\Phi)$ and $\mathcal{R}(\Phi)$ be classes of Ma-Minda starlike functions and bounded turning functions, respectively. In this article, we establish the sharp lower and upper bounds of initial coefficient differences for the functions in $\mathcal{S^{\ast }}(\Phi)$ and $\mathcal{R}(\Phi)$. We also obtain the bounds for the inverse coefficients, logarithmic, and inverse logarithmic coefficients for these classes. All the results we study are sharp.