Certain Subclasses of Starlike Functions of Complex Order Involving Generalized Hypergeometric Functions

Abstract EN

Making use of the generalized hypergeometric functions, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients and obtain coefficient estimates, extreme points, the radii of close-to-convexity, starlikeness and convexity, and neighborhood results for the class TSml(α,β,γ).

In particular, we obtain integral means inequalities for the function f that belongs to the class TSml(α,β,γ) in the unit disc.