Lemniscate starlikeness and convexity of Ramanujan entire-type function and its Alexander transform

Abstract

In this paper, we study the geometric behavior of a class of normalized Ramanujan entire-type functions and their Alexander transforms in the open unit disc. We establish new criteria ensuring that these functions are lemniscate starlike or lemniscate convex with respect to the right half of the Bernoulli lemniscate. Several illustrative examples are provided to demonstrate the behavior of the functions under the obtained conditions. These results contribute to a deeper understanding of the geometric properties of Ramanujan-type special functions.