Abstract
Let F be families of meromorphic functions in a domain D, and let R be a rational function whose degree is at least 3. If, for any f ∈ F, the composite function R(f) has no fixed-point in D, then f is normal in D. The number 3 is best possible. A new and much simplified proof of a result of Pang and Zalcman concerning normality and shared values is also given.
| Original language | English |
|---|---|
| Pages (from-to) | 307-321 |
| Number of pages | 15 |
| Journal | Arkiv for Matematik |
| Volume | 43 |
| Issue number | 2 |
| DOIs | |
| State | Published - Oct 2005 |
Bibliographical note
Funding Information:Acknowledgments. Jianming Chang would like to express his gratitude to his adviser Prof. Huaihui Chen for his many valuable suggestions. The research of Ming-liang Fang was supported by the NNSF of China (Grant No. 10471065), the SRF for ROCS, SEM., the Presidential Foundation of South China Agricultural University. The research of Lawrence Zalcman was supported by the German Israeli Foundation for Scientific Research and Development, G.I.F. (Grant No. G-643-117.6/1999).
Funding
Acknowledgments. Jianming Chang would like to express his gratitude to his adviser Prof. Huaihui Chen for his many valuable suggestions. The research of Ming-liang Fang was supported by the NNSF of China (Grant No. 10471065), the SRF for ROCS, SEM., the Presidential Foundation of South China Agricultural University. The research of Lawrence Zalcman was supported by the German Israeli Foundation for Scientific Research and Development, G.I.F. (Grant No. G-643-117.6/1999).
| Funders | Funder number |
|---|---|
| Presidential Foundation of South China Agricultural University | |
| German-Israeli Foundation for Scientific Research and Development | G-643-117.6/1999 |
| National Natural Science Foundation of China | 10471065 |