In this paper, we study certain classes of analytic functions which satisfy a subordination condition and are associated with the crescent-shaped regions.

In this paper, we study a class of strongly close-to-convex functions $f(z)$ analytic in the unit disk $\mathbb{U}$ with $f(0)=0,f^{\prime }(0)=1$ satisfying for some convex function $g(z)$ the condition that \begin{equation*} \frac{zf^{\prime }(z)}{g(z)}\prec \left( \frac{1+Az}{1+Bz}\right) ^{m} \end{equation*}% \begin{equation*} \left( -1\leq A\leq 1,-1\leq B\leq 1\ \left( A\neq B\right) ,0<m\leq 1;z\in \mathbb{U}\right) . \end{equation*}% We obtain for functions belonging to this class, the coefficient estimates, bounds, certain results based on an integral operator and radius of convexity. We also deduce a number of useful special cases and consequences of the various results which are presented in this paper.