(untitled) (European Journal of Pure and Applied Mathematics, 2025)
In this paper, we investigate the geometric behavior of the generalized normalized imaginary error function Υ i_k( z) and the associated convolution operator Ii_k(z) within the framework of analytic function theory. Specifically, we establish necessary and sufficient conditions under which these functions belong to the subclasses SPE(ϑ ,ζ ) and CSPE(ϑ,ζ ) of spirallike and convex spirallike analytic functions, respectively. Additionally, we derive sharp criteria for an integral operator involving Υ i_k( z) to be a member of these subclasses. These results extend and generalize several known findings and may inspire further applications of the imaginary error function in geometric function theory.