`Abstract and Applied AnalysisVolume 2009, Article ID 847690, 9 pageshttp://dx.doi.org/10.1155/2009/847690`
Research Article

## Uniqueness of Entire Functions Sharing Polynomials with Their Derivatives

1School of Mathematics and System Sciences, Shandong University, Jinan, Shandong 250100, China
2Department of Mathematics, China University of Petroleum, Dongying, Shandong 257061, China

Received 1 December 2008; Revised 10 April 2009; Accepted 6 May 2009

Copyright © 2009 Jianming Qi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. H.-X. Yi and C. C. Yang, Uniqueness Theory of Meromorphic Functions, Science Press, Beijing, China, 1995.
2. W. K. Hayman, Meromorphic Functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, UK, 1964.
3. L. A. Rubel and C. C. Yang, “Values shared by an entire function and its derivative,” in Complex Analysis, vol. 599 of Lecture Notes in Mathematics, pp. 101–103, Springer, Berlin, Germany, 1977.
4. E. Mues and N. Steinmetz, “Meromorphe Funktionen, die mit ihrer Ableitung Werte teilen,” Manuscripta Mathematica, vol. 29, no. 2–4, pp. 195–206, 1979.
5. J. Li and H.-X. Yi, “Normal families and uniqueness of entire functions and their derivatives,” Archiv der Mathematik, vol. 87, no. 1, pp. 52–59, 2006.
6. J.-P. Wang, “Entire functions that share a polynomial with their derivatives,” Journal of Mathematical Analysis and Applications, vol. 320, no. 2, pp. 703–717, 2006.
7. X.-M. Li and H.-X. Yi, “On uniqueness of an entire function and its derivatives,” Archiv der Mathematik, vol. 89, no. 3, pp. 216–225, 2007.
8. J. Grahl and C. Meng, “Entire functions sharing a polynomial with their derivatives and normal families,” Analysis, vol. 28, no. 1, pp. 51–61, 2008.
9. J. L. Schiff, Normal Families, Universitext, Springer, Berlin, Germany, 1993.
10. S. Li and S. Stević, “Riemann-Stieltjes-type integral operators on the unit ball in ${ℂ}^{n}$,” Complex Variables and Elliptic Equations, vol. 52, no. 6, pp. 495–517, 2007.
11. S. Stevich, “Boundedness and compactness of an integral operator in a mixed norm space on the polydisk,” Sibirskiĭ Matematicheskiĭ Zhurnal, vol. 48, no. 3, pp. 694–706, 2007.
12. L. Zalcman, “A heuristic principle in complex function theory,” The American Mathematical Monthly, vol. 82, no. 8, pp. 813–817, 1975.
13. J. Clunie and W. K. Hayman, “The spherical derivative of integral and meromorphic functions,” Commentarii Mathematici Helvetici, vol. 40, no. 1, pp. 117–148, 1966.