On some extremal problems on a class of univalent functions

Abstract

We investigate in this article the extremal problems max arg∫``(ζ),∫(z)∈S, and max arg∫(ζ),∫(z)∈$S_0$, where S is the class of all analytic and univalent functions ∫(z) in the unit disk, normalized by the conditions ∫(0)=0 and ∫``(0)=1, and $S_0$ the class of all nonvanishing, analytic and univalent functions ∫(z) in the unit disk, normalized by the condition ∫(0)=1. We also consider the growth theorem, the distortion theorem for the class $S_0(RHP)$, of all nonvanishing, analytic and univalent functions ∫(z) on the right half-plane which fix 1.