The Fekete-Szegő problem for strongly close-to-convex functions

Abstract:

Let $K(\beta )$ denote the class of normalized analytic strongly close-to-convex functions of order $\beta \geq 0$, defined in the unit disc $D$ and let $f \in K(\beta )$, with $f(z) = z + {a_2}{z^2} + {a_3}{z^3} + \cdots$, for $z \in D$. Sharp bounds are obtained for $|{a_3} - \mu a_2^2|$ when $\mu$ is real.