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

Abstract

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