Maximizing the generalized Fekete-Szego functional over a class of hyperbolically convex functions

In this paper, we are attempting to find an extremal for the "generalized" Fekete-Szego functional over the class of hyperbolically convex functions. In trying to find the extremal, the Julia variational formula will be used to reduce the problem to mappings having no more than two proper sides. We will then find a range of t-values for which the one-sided mapping is extremal over all those mappings having non-zero second coefficient.