AN THE ECUATION Re [(x-a)f(x)]=0, fєS

Abstract

Let S be the class of functions f(z)=z+a2z2…, f(0)=0, f′(0)=1 which are regular and univalent in theunit disk |z| x the equation φ′( x)=0 does not have real roots. Since S is acompact class, there exists x .This problem was first proposed by Petru T. Mocanu in [2]. We will determine x by using thevariational method of Schiffer-Goluzin [1].

Keywords

• function
• variation
• finite number