Geometric Characterizations of Imaginary Error Functions in Subclasses of Spirallike Analytic Functions (European Journal of Pure and Applied Mathematics, 2025)
In this paper, we investigate the geometric behavior of the generalized normalized imaginary error function $Υ i_{k}\left( z\right)$ and the associated convolution operator $\mathcal{I}i_{k}(z)$ within the framework of analytic function theory. Specifically, we establish necessary and sufficient conditions under which these functions belong to the subclasses $\mathcal{SPE}(ϑ ,ζ )$ and $\mathcal{CSPE}(ϑ,ζ )$ of spirallike and convex spirallike analytic functions, respectively. Additionally, we derive sharp criteria for an integral operator involving $Υ i_{k}\left( z\right)$ 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.
Keywords: Analytic; Univalent; Convex; Error function; Convex spirallike