On the Fekete–Szegö type functionals for functions which are convex in the direction of the imaginary axis

Abstract

In this paper we consider two functionals of the Fekete-Szegö type:) and for real numbers µ. For f which is univalent and convex in the direction of the imaginary axis, we find sharp bounds of the functionals Φ f (µ) and Θ f (µ). It is possible to transfer the results onto the class K R (i ) of functions convex in the direction of the imaginary axis with real coefficients as well as onto the class T of typically real functions. As corollaries, we obtain bounds of the second Hankel determinant in K R (i ) and T .