Roots of the equationf (z)=αf (α) for the class of typically-real functions

Name: Roots of the equationf (z)=αf (α) for the class of typically-real functions
Creator: Burshtejn, L. Kh.
Keywords: Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.), Conformal mappings of special domains

Burshtejn, L. Kh.

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Mathematical Notes

Article . 1971 . Peer-reviewed

License: Springer TDM

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Article . 1972

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https://dx.doi.org/10.1007/bf0...

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Roots of the equationf (z)=αf (α) for the class of typically-real functions

Roots of the equation \(f(z) = \alpha f(a)\) for the class of typiclally- real functions

descriptionPublicationkeyboard_double_arrow_right Article 01 Jul 1971 English Publisher:Springer Science and Business Media LLCJournal:Mathematical Notes of the Academy of Sciences of the USSR, volume 10, pages 449-455 (issn: 0001-4346, eissn: 1573-8876,

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Authors: Burshtejn, L. Kh.;

doi: 10.1007/bf01747068

Roots of the equationf (z)=αf (α) for the class of typically-real functions

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Abstract

Let Tr be the class of functionsf (z)=z+c2z2+..., regular in the disk ¦z¦ 0 in the remainder of the disk ¦z¦ <1. Let z f be the solution off (z)=αf (a) on Tr, whereα is any fixed complex numberα ≠ 0,α ≠ 1,α is any fixed real number, ¦α¦< 1. We determine the region\(D_{T_r } \) of values of the functional zf on the class Tr. Variation formulas for Stieltjes integrals due to G.M. Goluzin are used.

Related Organizations

Oriental University
Russian Federation

Keywords

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.), Conformal mappings of special domains

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