Geometric Properties of Generalized Janowski Type Functions

The present paper aims to explore subclasses of analytic functions that extend the class of Janowski-type functions. We examine specific convolution conditions that ensure functions h fall within the generalized Janowski-type classes of starlike and convex functions. These conditions will serve as foundational results for further analysis in this study. Additionally, we provide sufficient conditions and neighborhood results pertinent to functions within the starlike class. Finally, we investigate the invariance properties of the operator hμ(ϑ) = (1 − μ)ϑ + μh(ϑ), 0 < μ < 1, as it applies to functions in this classification.