Coefficient estimates for Ruscheweyh derivatives

Coefficient estimates for Ruscheweyh derivatives

are classes of starlike and strongly starlike functions of order β (0 < β ≤ 1), respectively. Note that S∗(β)⊂ S∗ for 0< β< 1 and S∗(1)= S∗ [5]. Kanas [2] introduced the subclass R̄δ(β) of function f ∈ S as the following. Definition 1.1. For δ ≥ 0, β ∈ (0,1], a function f normalized by (1.1) belongs to R̄δ(β) if, for z ∈D−{0} and Dδf(z)≠ 0, the following holds: ∣∣∣arg z ( Dδf(z) )′ Dδf(z) ∣∣∣≤ βπ...

Univalent Functions Defined by Ruscheweyh Derivatives

We study some radii problems concerning the integral operator z F(z)y+l uY-I f(u) du zy o for certain classes, namely K and M (a), of univalent functions defined by Ruscheweyh n n derivatives. Infact, we obtain the converse of Ruscheweyh’s result and improve a result of Goel and Sohi for complex by a different technique. The results are sharp.

Coefficient Estimates for Univalent Functions

Subclasses of α-spirallike functions associated with Ruscheweyh derivatives

Properties of Certain Multivalent Functions Involving Ruscheweyh Derivatives

Let Ap(p ∈ N) be the class of functions f(z) = z + ∑∞ m=1 ap+mz p+m which are analytic in the unit disk. By virtue of the Ruscheweyh derivatives we introduce the new subclasses Cp(n, α, β, λ, μ) of Ap. Subordination relations, inclusion relations, convolution properties and a sharp coefficient estimate are obtained. We also give a sufficient condition for a function to be in Cp(n, α, β, λ, μ).