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In this paper we define a method of symmetrization for plane domains that includes as special cases methods of symmetrization considered by Szegö and by Marcus. We prove that under this method of symmetrization the mapping radius of a fixed point is not decreased. This fact is used to obtain some results concerning covering properties of Bieberbach-Eilenberg functions. We define (2.3) RS"\) = #»>(, A, B) = n*(a^+&)| Lfc = l J llndoi:10.1090/s0002-9947-1972-0291423-x fatcat:4kbetjhapfbhthhkidvcm43fba