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For α ∈ C\{0} let E(α) denote the class of all univalent functions f in the unit disk D and is given by f (z) = z + a2z2 + a3z3 +· · · , satisfying Re 1 + z f (z) f (z) + αz f (z) >0 inD. For any fixed z0 in the unit disk D and λ ∈ D, we determine the region of variability V(z0, λ) for log f (z0) + αf (z0) when f ranges over the class Fα(λ) = f ∈ E(α) : f (0) = 2λ − α . 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.
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