Goluzin's extension of the Schwarz-Pick inequality
<p/> <p>For a function <inline-formula><graphic file="1029-242X-1997-781962-i1.gif"/></inline-formula> holomorphic and bounded, <inline-formula><graphic file="1029-242X-1997-781962-i2.gif"/></inline-formula>, with the expansion <...
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
1997-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/1/781962 |
| _version_ | 1819057617263132672 |
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| author | Yamashita Shinji |
| author_facet | Yamashita Shinji |
| author_sort | Yamashita Shinji |
| collection | DOAJ |
| description | <p/> <p>For a function <inline-formula><graphic file="1029-242X-1997-781962-i1.gif"/></inline-formula> holomorphic and bounded, <inline-formula><graphic file="1029-242X-1997-781962-i2.gif"/></inline-formula>, with the expansion <inline-formula><graphic file="1029-242X-1997-781962-i3.gif"/></inline-formula> in the disk <inline-formula><graphic file="1029-242X-1997-781962-i4.gif"/></inline-formula>, we set <inline-formula><graphic file="1029-242X-1997-781962-i5.gif"/></inline-formula> Goluzin's extension of the Schwarz-Pick inequality is that <inline-formula><graphic file="1029-242X-1997-781962-i6.gif"/></inline-formula> We shall further improve Goluzin's inequality with a complete description on the equality condition. For a holomorphic map from a hyperbolic plane domain into another, one can prove a similar result in terms of the Poincaré metric.</p> |
| first_indexed | 2024-12-21T13:42:09Z |
| format | Article |
| id | doaj.art-34eba5710915400bbc46ab740c546df0 |
| institution | Directory Open Access Journal |
| issn | 1025-5834 1029-242X |
| language | English |
| last_indexed | 2024-12-21T13:42:09Z |
| publishDate | 1997-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-34eba5710915400bbc46ab740c546df02022-12-21T19:01:59ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X1997-01-0119974781962Goluzin's extension of the Schwarz-Pick inequalityYamashita Shinji<p/> <p>For a function <inline-formula><graphic file="1029-242X-1997-781962-i1.gif"/></inline-formula> holomorphic and bounded, <inline-formula><graphic file="1029-242X-1997-781962-i2.gif"/></inline-formula>, with the expansion <inline-formula><graphic file="1029-242X-1997-781962-i3.gif"/></inline-formula> in the disk <inline-formula><graphic file="1029-242X-1997-781962-i4.gif"/></inline-formula>, we set <inline-formula><graphic file="1029-242X-1997-781962-i5.gif"/></inline-formula> Goluzin's extension of the Schwarz-Pick inequality is that <inline-formula><graphic file="1029-242X-1997-781962-i6.gif"/></inline-formula> We shall further improve Goluzin's inequality with a complete description on the equality condition. For a holomorphic map from a hyperbolic plane domain into another, one can prove a similar result in terms of the Poincaré metric.</p>http://www.journalofinequalitiesandapplications.com/content/1/781962Bounded holomorphic functionsSchwarz's inequalityPoincaré density |
| spellingShingle | Yamashita Shinji Goluzin's extension of the Schwarz-Pick inequality Journal of Inequalities and Applications Bounded holomorphic functions Schwarz's inequality Poincaré density |
| title | Goluzin's extension of the Schwarz-Pick inequality |
| title_full | Goluzin's extension of the Schwarz-Pick inequality |
| title_fullStr | Goluzin's extension of the Schwarz-Pick inequality |
| title_full_unstemmed | Goluzin's extension of the Schwarz-Pick inequality |
| title_short | Goluzin's extension of the Schwarz-Pick inequality |
| title_sort | goluzin s extension of the schwarz pick inequality |
| topic | Bounded holomorphic functions Schwarz's inequality Poincaré density |
| url | http://www.journalofinequalitiesandapplications.com/content/1/781962 |
| work_keys_str_mv | AT yamashitashinji goluzinsextensionoftheschwarzpickinequality |