$Norm estimates for the class of $k$-uniformly convex and $k$-starlike functions of order $\alpha

For a constant $0 k 1$ and $\alpha 1$, we define the class of $k$-Uniformly convex and $k$-Starlike functions of order $\alpha$; $K(k,\alpha)$ and $S^*(k,\alpha)$ respectively; and give the best estimate for the norm of the pre-Schwarzian derivative in $K(k,\alpha)$ and $S^*(k,\alpha)$.