Let
$${\mathcal S}$$
denote the class of all functions of the form
$${f(z)=z+a_2z^2+a_3z^3+\cdots}$$
which are analytic and univalent in the open unit disk
$${{\mathbb{D}} }$$
and, for
$${\lambda > 0}$$
, let
$${\Phi_\lambda (n,f)=\lambda a_n^2-a_{2n-1}}$$
denote the generalized Zalcman coefficient functional. Zalcman conjectured that if
$${f\in \mathcal S}$$
, then
$${|\Phi_1 (n,f)|\leq (n-1)^2}$$
for
$${{n\ge 3}}$$
. The fun...
