  We obtain sharp estimates for a generalized Zalcman coefficient functional
with a complex parameter for the Hurwitz class and the Noshiro-Warschawski
class of univalent functions as well as for the closed convex hulls of the
convex and starlike functions by using an inequality from [6]. In particular,
we generalize an inequality proved by Ma for starlike functions and answer a
question from his paper [16]. Finally, we prove an asymptotic version of the
generalized Zalcman conjecture for univalent functions and discuss various
related or equivalent statements which may shed further light on the problem.
