A Novel Subclass of Analytic Univalent Functions Linked to Hypergeometric Functions

Abstract

This paper introduces a novel subclass of analytic univalent functions defined within the unit disk, with a particular association to hypergeometric functions. The subclass is formulated by applying a specific linear operator on a well-known class of analytic functions. The primary aim is to investigate the geometric properties of these functions, including coefficient bounds, distortion inequalities, and closure theorems. Additionally, the subclass is shown to generalize several well-known classes of univalent functions, providing a broader framework for understanding their behaviors. The connection with hypergeometric functions allows for the application of classical techniques in complex analysis to derive these properties, thereby offering a new perspective on the role of special functions in geometric function theory. The results presented in this study contribute to the ongoing research in the field, offering potential applications in various areas such as geometric function theory, mathematical physics, and engineering. The findings also open up new avenues for further exploration, particularly in the extension of these results to more general domains and the examination of other classes of special functions within this new framework.