The Second Hankel Determinant of Logarithmic Coefficients for Starlike and Convex Functions Involving Four-Leaf-Shaped Domain

Abstract

In this particular research article, we take an analytic function $Q_{4\mathcal{L}}=1+5/6z+1/6z^5$ , which makes a four-leaf-shaped image domain. Using this specific function, two subclasses, ${\mathcal{S}}_{4\mathcal{L}}^{\ast }$ and ${\mathcal{C}}_{4\mathcal{L}}$ , of starlike and convex functions will be defined. For these classes, our aim is to find some sharp bounds of inequalities that consist of logarithmic coefficients. Among the inequalities to be studied here are Zalcman inequalities, the Fekete-Szegö inequality, and the second-order Hankel determinant.