  In this article we consider a family $\mathcal{C}(A, B)$ of analytic and
locally univalent functions on the open unit disc $\ID=\{z :|z|<1\}$ in the
complex plane that properly contains the well-known Janowski class of convex
univalent functions. In this article, we determine the exact set of variability
of $\log(f'(z_0))$ with fixed $z_0 \in \ID$ and $f"(0)$ whenever $f$ varies
over the class $\mathcal{C}(A, B)$.
