For alpha is an element of C{0} let epsilon(alpha) denote the class of all univalent functions f in the unit disk D and is given by f (z) = z + a(2)z(2) + a(3)z(3) + ... , satisfying Re(1+ zf ''(z)/f'(z) + alpha zf'(z)) > 0 in D. For any fixed z(0) in the unit disk D and lambda is an element of (D) over bar, we determine the region of variability V(z(0), lambda) for log f' (z(0)) + alpha f (z(0)) when f ranges over the class F(alpha)(lambda) = {f is an element of epsilon(alpha): f ''(0) = 2 lambda - alpha}. We geometrically illustrate the region of variability V(z(0), lambda) for several sets of parameters using Mathematica. In the final section of this article we propose some open problems.
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