Holomorphic mappings of the unit disc into itself with two fixed points
The paper is concerned with holomorphic mappings of the unit disc into itself with two fixed points. Two cases are considered: when one fixed point lies inside the disc and the other lies on the boundary and when both fixed points lie on the boundary. The effect that angular derivatives at boundary...
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| Veröffentlicht in: | Sbornik. Mathematics 2017-03, Vol.208 (3), p.360-376 |
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| container_end_page | 376 |
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| container_title | Sbornik. Mathematics |
| container_volume | 208 |
| creator | Goryainov, V. V. |
| description | The paper is concerned with holomorphic mappings of the unit disc into itself with two fixed points. Two cases are considered: when one fixed point lies inside the disc and the other lies on the boundary and when both fixed points lie on the boundary. The effect that angular derivatives at boundary fixed points have on the properties of functions inside the unit disc is studied. Conditions on the angular derivatives to guarantee the existence of domains of univalence inside the unit disc are given. The effect of the angular derivatives on the values of the Taylor coefficients of functions is also examined. Bibliography: 19 titles. |
| doi_str_mv | 10.1070/SM8802 |
| format | Article |
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Math</addtitle><date>2017-03-01</date><risdate>2017</risdate><volume>208</volume><issue>3</issue><spage>360</spage><epage>376</epage><pages>360-376</pages><issn>1064-5616</issn><eissn>1468-4802</eissn><abstract>The paper is concerned with holomorphic mappings of the unit disc into itself with two fixed points. Two cases are considered: when one fixed point lies inside the disc and the other lies on the boundary and when both fixed points lie on the boundary. The effect that angular derivatives at boundary fixed points have on the properties of functions inside the unit disc is studied. Conditions on the angular derivatives to guarantee the existence of domains of univalence inside the unit disc are given. The effect of the angular derivatives on the values of the Taylor coefficients of functions is also examined. 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| fulltext | fulltext |
| identifier | ISSN: 1064-5616 |
| ispartof | Sbornik. Mathematics, 2017-03, Vol.208 (3), p.360-376 |
| issn | 1064-5616 1468-4802 |
| language | eng |
| recordid | cdi_iop_journals_10_1070_SM8802 |
| source | Institute of Physics Journals; Alma/SFX Local Collection |
| subjects | angular derivative coefficient region Derivatives domain of univalence fixed point Fixed points (mathematics) holomorphic mapping Mathematical analysis |
| title | Holomorphic mappings of the unit disc into itself with two fixed points |
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