Starlikeness associated with lemniscate of Bernoulli

Abstract

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