The connection between the geometric versions of Schwarz’s lemma and the known symmetrization principles for some classes of analytic functions in a disk and a circular ring are discussed. In particular, simple proofs based on classical approaches are presented for some recent results of other authors. Bibliography: 22 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 383, 2010, pp. 63–76.
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Dubinin, V.N. Geometric versions of Schwarz’s lemma and symmetrization. J Math Sci 178, 150–157 (2011). https://doi.org/10.1007/s10958-011-0542-0
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DOI: https://doi.org/10.1007/s10958-011-0542-0