Hankel determinant for starlike and convex functions of order alpha

Abstract

The objective of this paper is to obtain an upper bound to the second Hankel determinant $|a_{2}a_{4}-a_{3}^{2}|$ for starlike and convex functions of order $\alpha$ $(0\leq\alpha\lt1)$, also for the inverse function of $f$, belonging to the class of convex functions of order $\alpha$, using Toeplitz determinants.