The Fekete-Szego problem by a variational method

Abstract

The article is devoted to the well-known Fekete and Szego problem. The paper investigate the problem in sufficient detail using some new observations by the classical method of internal variations, developed at the Tomsk School of Complex Analysis. One particular case is considered. We carried out complete qualitative analysis of the functional-differential equation relative boundary mapping. We completely solved the problem for the real parameter.