Applications of Livingston‐type inequalities to the generalized Zalcman functional

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 17]. 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.