Journal of the
Korean Mathematical Society JKMS

In \cite{Rusche1,Rusche2} the researchers introduced universally convex, universally starlike and universally prestarlike functions in the slit domain $\mathbb{C}\backslash \lbrack 1,\infty )$. These papers extended the corresponding notions from the unit disc to other discs and half-planes containing the origin. In this paper, we introduce universally prestarlike generalized functions of order $\alpha $ with $\alpha \leq 1$ and we obtain upper bounds of the second Hankel determinant $|a_{2}a_{4}-a_{3}^{2}|$ for such functions.

Keywords: analytic functions, prestarlike functions, universally prestarlike functions, second Hankel determinant

MSC numbers: Primary 30C45