AN EXTREMAL PROBLEM FOR UNIVALENT FUNCTIONS

Abstract

Let S be the class of functions f(z)=z+a2z 2 …, f(0)=0, f′(0)=1 which are regular and univalent in the unit disk |z| x the equation φ′( x)=0 does not have real roots. Since S is a compact class, there exists x . This problem was first proposed by Petru T. Mocanu in [2]. We will determine x by using the variational method of Schiffer-Goluzin [1].

Keywords

• extremal function
• regular
• univalent