Generalized k-Uniformly Close-to-Convex Functions Associated with Conic Regions

Abstract EN

We define and study some subclasses of analytic functions by using a certain multiplier transformation.

These functions map the open unit disc onto the domains formed by parabolic and hyperbolic regions and extend the concept of uniformly close-to-convexity.

Some interesting properties of these classes, which include inclusion results, coefficient problems, and invariance under certain integral operators, are discussed.

The results are shown to be the best possible.