On Some Results for -spirallike and -robertson Functions of Complex Order
Let A denote the class of normalized analytic functions in the unit disc U = z: |z| < 1. The author obtains fixed values of δ and ϱ (δ ≈ 0.308390864..., ϱ ≈ 0.0903572...) such that the integral transforms F and G defined by and are starlike (univalent) in U, whenever f ∈ A and g ∈ A satisfy Ref’(z) > -δ and Re g’(z) > -ϱ respectively in U.
H. Silverman (1999) investigated the properties of functions defined in terms of the quotient of the analytic representations of convex and starlike functions. Many research workers have been working on analytic functions to be strongly starlike like Obradović and Owa (1989), Takahashi and Nunokawa (2003), Lin (1993) etc. In this paper we obtain a sufficient condition for -valent functions to be strongly starlike of order .