Starlikness Associated with Euler Numbers

Let $\psi _{E}\left(
z\right) =\sec h\left(
z\right)
=\underset{n=0}{\overset%
{\infty }{\sum
}}\frac{E_{n}}{n!}z^{n},$ where the
constants $E_{n}$ are Euler numbers. The class
$\mathcal{S}_{E}^{\ast }$
denote the class of normalized analytic functions $f$ satisfying
$zf^{\prime }(z)/f(z)\prec
\psi _{E}\left( z\right)
$. For this class, we obtain structural formula, inclusion results, and
some sharp radii problems such as radius of convexity, radius for the
class of Janowski starlike functions and radius for some other
subclasses of starlike functions. We also find sharp coefficient results
and sharp Hankel determinants for functions in the class
$\mathcal{S}_{E}^{\ast }.$