In [12,13] the researchers introduced universally convex, universally starlike and universally prestarlike functions in the slit domain ℂ\[1, ∞). 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 α with α ≤ 1 and we obtain upper bounds of the second Hankel determinant |a2a4 − a2 3 | for such functions. © 2018 Korean Mathematical Society.