Coefficient Inequalities for Starlikeness and Convexity
  For an analytic function f(z)=z+\sum_{n=2}^\infty a_n z^n satisfying the inequality \sum_{n=2}^\infty n(n-1)|a_n|\leq \beta, sharp bound on $\beta$ is determined so that $f$ is either starlike or convex of order $\alpha$. Several other coefficient inequalities related to certain subclasses are also investigated. 
Rosihan M. Ali, Moradi Nargesi Mahnaz, V. Ravichandran
math.CV