Computational Methods and Function Theory 3 (2003), No. 2, 485--499
Copyright Heldermann Verlag 2003
Alexander Kuznetsov
kuznetsovaa@pisem.net , Department of Mathematics and Mechanics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov, Russia.
In this paper we consider the problem of approximation of holomorphic univalent functions by compositions of the Pick functions. For functions f in the class S of univalent holomorphic functions in the unit disk normalized by f(0) = f'(0) - 1 = 0, an estimate of the rate of approximation by means of compositions is obtained.
Keywords: Univalent functions, composition, approximation, Loewner-Kufarev equation.
MSC 2000: 30C55, 30C35.
[FullText-pdf (336 K)] [FullText-ps (288 K)]