Dynamics of inequalities in geometric function theory
<p/> <p>A domain in the complex plane which is star-like with respect to a boundary point can be approximated by domains which are star-like with respect to interior points. This approximation process can be viewed dynamically as an evolution of the null points of the underlying holomorp...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2001-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/6/454268 |
| _version_ | 1818979816804712448 |
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| author | Reich Simeon Elin Mark Shoikhet David |
| author_facet | Reich Simeon Elin Mark Shoikhet David |
| author_sort | Reich Simeon |
| collection | DOAJ |
| description | <p/> <p>A domain in the complex plane which is star-like with respect to a boundary point can be approximated by domains which are star-like with respect to interior points. This approximation process can be viewed dynamically as an evolution of the null points of the underlying holomorphic functions from the interior of the open unit disk towards a boundary point. We trace these dynamics analytically in terms of the Alexander–Nevanlinna and Robertson inequalities by using the framework of complex dynamical systems and hyperbolic monotonicity.</p> |
| first_indexed | 2024-12-20T17:05:33Z |
| format | Article |
| id | doaj.art-1441d6c5870340938fc18d1e6afe99ea |
| institution | Directory Open Access Journal |
| issn | 1025-5834 1029-242X |
| language | English |
| last_indexed | 2024-12-20T17:05:33Z |
| publishDate | 2001-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-1441d6c5870340938fc18d1e6afe99ea2022-12-21T19:32:18ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2001-01-0120016454268Dynamics of inequalities in geometric function theoryReich SimeonElin MarkShoikhet David<p/> <p>A domain in the complex plane which is star-like with respect to a boundary point can be approximated by domains which are star-like with respect to interior points. This approximation process can be viewed dynamically as an evolution of the null points of the underlying holomorphic functions from the interior of the open unit disk towards a boundary point. We trace these dynamics analytically in terms of the Alexander–Nevanlinna and Robertson inequalities by using the framework of complex dynamical systems and hyperbolic monotonicity.</p>http://www.journalofinequalitiesandapplications.com/content/6/454268Cauchy problemPoincaré metricStar-like functionUnivalent holomorphic function |
| spellingShingle | Reich Simeon Elin Mark Shoikhet David Dynamics of inequalities in geometric function theory Journal of Inequalities and Applications Cauchy problem Poincaré metric Star-like function Univalent holomorphic function |
| title | Dynamics of inequalities in geometric function theory |
| title_full | Dynamics of inequalities in geometric function theory |
| title_fullStr | Dynamics of inequalities in geometric function theory |
| title_full_unstemmed | Dynamics of inequalities in geometric function theory |
| title_short | Dynamics of inequalities in geometric function theory |
| title_sort | dynamics of inequalities in geometric function theory |
| topic | Cauchy problem Poincaré metric Star-like function Univalent holomorphic function |
| url | http://www.journalofinequalitiesandapplications.com/content/6/454268 |
| work_keys_str_mv | AT reichsimeon dynamicsofinequalitiesingeometricfunctiontheory AT elinmark dynamicsofinequalitiesingeometricfunctiontheory AT shoikhetdavid dynamicsofinequalitiesingeometricfunctiontheory |