Back to Search
Start Over
Entire functions that have the same fixed points with their first derivatives
- Source :
-
Journal of Mathematical Analysis & Applications . Feb2004, Vol. 290 Issue 1, p235. 12p. - Publication Year :
- 2004
-
Abstract
- Let <f>f</f> be a nonconstant entire function, and let <f>k</f> <f>(&ges;2)</f> be an integer. We denote by <f>Ef(z)={z∈C: f(z)=z, counting multiplicities}</f> the set consisting of all the fixed points of <f>f</f>. This paper proves that if <f>f</f> and <f>f′</f> have the same fixed points, namely, <f>Ef(z)=Ef′(z)</f>, and if <f>f(k)(z)=z</f> whenever <f>f(z)=z</f>, then <f>f≡f′</f>. [Copyright &y& Elsevier]
- Subjects :
- *INTEGRAL functions
*COMPLEX variables
*SET theory
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 0022247X
- Volume :
- 290
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 11960639
- Full Text :
- https://doi.org/10.1016/j.jmaa.2003.09.050