Inclusion Criteria for Subclasses of Functions and Gronwall's Inequality
  A normalized analytic function f is shown to be univalent in the open unit disk D if its second coefficient is sufficiently small and relates to its Schwarzian derivative through a certain inequality. New criteria for analytic functions to be in certain subclasses of functions are established in terms of the Schwarzian derivatives and the second coefficients. These include obtaining a sufficient condition for functions to be strongly $\alpha$-Bazilevi\^c of order $\beta$. 
Rosihan M. Ali, Mahnaz M. Nargesi, V. Ravichandran, A. Swaminathan
math.CV