Region of Variability for Exponentially Convex Univalent Functions

For α ∈ ℂ\{0} let ε(α) denote the class of all univalent functions f in the unit disk D and is given by f(z) = z + a2Z2 + a3Z3 + ..., satisfying, For any fixed z0 in the unit disk D and λ ∈ D̄ we determine the region of variability V(z0, λ) for log f′(z0) + αf(z0) when f ranges over the class, We geometrically illustrate the region of variability V(z0, λ) for several sets of parameters using Mathematica. In the final section of this article we propose some open problems. © 2010 Springer Basel AG.