  We consider certain subfamilies, of the family of univalent functions in the
open unit disk, defined by means of sufficient coefficient conditions for
univalency. This article is devoted to studying the problem of the well-known
conjecture of Zalcman consisting of a generalized coefficient functional, the
so-called generalized Zalcman conjecture problem, for functions belonging to
those subfamilies. We estimate the bounds associated with the generalized
coefficient functional and show that the estimates are sharp.
