Iovanov, Miodrag Determining of an extremal domain fo the functions from the \(S\)-class. (English) Zbl 1114.30301 Acta Univ. Apulensis, Math. Inform. 7, 135-148 (2004). Summary: Let \(S\) be the class of analytic functions of the form \(f(z)=z+a_2z^2+\dots\), \(f(0)=0\), \(f^\prime(0)=1\) defined on the unit disk \(| z|<1\). Petru T. Mocanu raised the question of the determination max Re \(f(z)\) when Re \( f^\prime(z)=0\), \(| z|=r\), \(r>0\) given. For solving the problem we shall use the variational method of Schiffer-Goluzin [G. M. Goluzin, Geometrische Theorie der Funktionen einer komplexen Veränderlichen. Moskau-Leningrad: Staatsverlag für technisch-theoretische Literatur (1952; Zbl 0049.05902)]. MSC: 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) Keywords:univalent functions; variational methods; Schiffer-Goluzin; extremal functions Citations:Zbl 0049.05902 PDFBibTeX XMLCite \textit{M. Iovanov}, Acta Univ. Apulensis, Math. Inform. 7, 135--148 (2004; Zbl 1114.30301) Full Text: EuDML