  Let $\mathcal{S}$ denote the family of all functions that are analytic and
univalent in the unit disk $\mathbb{D}:=\{z: |z|<1\}$ and satisfy
$f(0)=f^{\prime}(0)-1=0$. In the present paper, we consider certain subclasses
of univalent functions associated with the exponential function, and obtain the
sharp upper bounds on the initial coefficients and the difference of initial
successive coefficients for functions belonging to these classes.
