Second Hankel determinant for universally prestarlike functions related with exponential function

In Ruscheweyh and Salinas (Math Z 263:607–617, 2009) and Ruscheweyh et al. (Isreal J Math 171:285–304, 2009) the researchers introduced universally convex,universally starlike and universally prestarlike functions in the slit domain $$ {\mathbb {C}}\backslash [1,\infty {)}.$$ These papers extended the corresponding notions from the unit disc to other discs and half-planes containing the origin. In this paper, we consider universally prestarlike generalized functions of order $$\alpha $$ with $$\alpha \le 1$$ and we obtain upper bounds of the second Hankel determinant $$|a_{2}a_{4}-a_{3}^{2}|$$ for such functions related with exponential function.