Sharp coefficient Estimates for the class ${\mathcal{S}}_{\mathcal{A}\mathcal{P}}^{\ast }$

Abstract

We investigate several classic coefficient problems for the Ma--Minda starlike subclass ${\mathcal{S}}_{\mathcal{A}\mathcal{P}}^{\ast }$ defined by the apple-like subordination function ${\psi }_{\mathcal{A}\mathcal{P}}(z)=e^z\sqrt{1+z}$. Sharp bounds are derived for the initial inverse logarithmic coefficients ${\Gamma }_1$, ${\Gamma }_2$, ${\Gamma }_3$, and the successive modulus difference $|{\Gamma }_2|-|{\Gamma }_1|$. In addition, we evaluate the second-order inverse logarithmic Hankel determinant, the generalized Fekete--Szegö functional over all real parameter domains, and the third-order Hermitian--Toeplitz determinant. The corresponding extremal functions are explicitly determined for each functional.

arXiv comment21 pages,4 figures and 1 table