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Fixed points of composite meromorphic functions and normal families
| Content Provider | Scilit |
|---|---|
| Author | Bergweiler, Walter |
| Copyright Year | 2004 |
| Description | We show that there exists a function f, meromorphic in the plane C, such that the family of all functions g holomorphic in the unit disc D for which f ∘ g has no fixed point in D is not normal. This answers a question of Hinchliffe, who had shown that this family is normal if Ĉ\f(C) does not consist of exactly one point in D. We also investigate the normality of the family of all holomorphic functions g such that f(g(z)) ≠ h(z) for some non-constant meromorphic function h. |
| Related Links | http://analysis.math.uni-kiel.de/bergweiler/papers/69a.pdf https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A1882005BC398A5FBA26DF21D57AA83C/S0308210500003401a.pdf/div-class-title-fixed-points-of-composite-meromorphic-functions-and-normal-families-div.pdf |
| Ending Page | 660 |
| Page Count | 8 |
| Starting Page | 653 |
| ISSN | 03082105 |
| e-ISSN | 14737124 |
| DOI | 10.1017/s0308210500003401 |
| Journal | Proceedings of the Royal Society of Edinburgh: Section A Mathematics |
| Issue Number | 4 |
| Volume Number | 134 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2004-08-01 |
| Access Restriction | Open |
| Subject Keyword | Section A Mathematics Applied Mathematics Meromorphic Functions No Fixed Composite Meromorphic Unit Disc Constant Meromorphic Normality of the Family |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
