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 C\[1, infinity). 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 <= 1 and we obtain upper bounds of the second Hankel determinant vertical bar a(2)a(4) - a(3)(2)vertical bar for such functions related with exponential function.