On the theorem of wan for K-quasiconformal hyperbolic harmonic self mappings of the unit disk
We give a new glance to the theorem of Wan (Theorem 1.1) which is related to the hyperbolic bi-Lipschicity of the K-quasiconformal, K ≥ 1, hyperbolic harmonic mappings of the unit disk D onto itself. Especially, if f is such a mapping and f(0) = 0, we obtained that the following double inequality is...
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| Format: | Article |
| Language: | English |
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University of Kragujevac, Faculty of Technical Sciences Čačak
2015-01-01
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| Series: | Mathematica Moravica |
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| Online Access: | http://scindeks-clanci.ceon.rs/data/pdf/1450-5932/2015/1450-59321501081K.pdf |
| _version_ | 1827092674813886464 |
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| author | Knežević Miljan |
| author_facet | Knežević Miljan |
| author_sort | Knežević Miljan |
| collection | DOAJ |
| description | We give a new glance to the theorem of Wan (Theorem 1.1) which is related to the hyperbolic bi-Lipschicity of the K-quasiconformal, K ≥ 1, hyperbolic harmonic mappings of the unit disk D onto itself. Especially, if f is such a mapping and f(0) = 0, we obtained that the following double inequality is valid 2│z│=(K + 1) ≤ │f(z)│ ≤ √ K│z│, whenever z _ D. |
| first_indexed | 2024-04-13T19:21:22Z |
| format | Article |
| id | doaj.art-66ddb61c93564e58bb118f7890ae7710 |
| institution | Directory Open Access Journal |
| issn | 1450-5932 2560-5542 |
| language | English |
| last_indexed | 2025-03-20T06:15:57Z |
| publishDate | 2015-01-01 |
| publisher | University of Kragujevac, Faculty of Technical Sciences Čačak |
| record_format | Article |
| series | Mathematica Moravica |
| spelling | doaj.art-66ddb61c93564e58bb118f7890ae77102024-10-02T17:28:24ZengUniversity of Kragujevac, Faculty of Technical Sciences ČačakMathematica Moravica1450-59322560-55422015-01-0119181851450-59321501081KOn the theorem of wan for K-quasiconformal hyperbolic harmonic self mappings of the unit diskKnežević Miljan0Faculty of Mathematics, BelgradeWe give a new glance to the theorem of Wan (Theorem 1.1) which is related to the hyperbolic bi-Lipschicity of the K-quasiconformal, K ≥ 1, hyperbolic harmonic mappings of the unit disk D onto itself. Especially, if f is such a mapping and f(0) = 0, we obtained that the following double inequality is valid 2│z│=(K + 1) ≤ │f(z)│ ≤ √ K│z│, whenever z _ D.http://scindeks-clanci.ceon.rs/data/pdf/1450-5932/2015/1450-59321501081K.pdfhyperbolic metricharmonic mappingsquasiconformal mappings |
| spellingShingle | Knežević Miljan On the theorem of wan for K-quasiconformal hyperbolic harmonic self mappings of the unit disk Mathematica Moravica hyperbolic metric harmonic mappings quasiconformal mappings |
| title | On the theorem of wan for K-quasiconformal hyperbolic harmonic self mappings of the unit disk |
| title_full | On the theorem of wan for K-quasiconformal hyperbolic harmonic self mappings of the unit disk |
| title_fullStr | On the theorem of wan for K-quasiconformal hyperbolic harmonic self mappings of the unit disk |
| title_full_unstemmed | On the theorem of wan for K-quasiconformal hyperbolic harmonic self mappings of the unit disk |
| title_short | On the theorem of wan for K-quasiconformal hyperbolic harmonic self mappings of the unit disk |
| title_sort | on the theorem of wan for k quasiconformal hyperbolic harmonic self mappings of the unit disk |
| topic | hyperbolic metric harmonic mappings quasiconformal mappings |
| url | http://scindeks-clanci.ceon.rs/data/pdf/1450-5932/2015/1450-59321501081K.pdf |
| work_keys_str_mv | AT knezevicmiljan onthetheoremofwanforkquasiconformalhyperbolicharmonicselfmappingsoftheunitdisk |