Starlikeness associated with lemniscate of Bernoulli

For an analytic function $f$ on the unit disk $\mathbb{D}=\{z:\mathrm{\mid }z\mathrm{\mid }<1\}$ satisfying $f(0)=0=f^{\mathrm{\prime }}(0)-1,$ we obtain sufficient conditions so that $f$ satisfies $\mathrm{\mid }(z{f}^{\mathrm{\prime }}(z)\mathrm{/}f(z){)}^2-1\mathrm{\mid }<1.$ The technique of differential subordination of first or second order is used. The admissibility conditions for lemniscate of Bernoulli are derived and employed in order to prove the main results.