JOURNAL BROWSE
Search
Advanced SearchSearch Tips
A NOTE ON THE HYPER-ORDER OF ENTIRE FUNCTIONS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
A NOTE ON THE HYPER-ORDER OF ENTIRE FUNCTIONS
Lu, Feng; Qi, Jianming;
  PDF(new window)
 Abstract
In the paper, we have two purposes. Firstly, we estimate the hyper-order of an entire function which shares two functions with it's first derivative, and two examples are given to show the conclusion is sharp. Secondly, we generalize the Brck conjecture with the idea of sharing functions.
 Keywords
complex differential equation;normal family;Nevanlinna theory;
 Language
English
 Cited by
1.
Growth of Meromorphic Function Sharing Functions and Some Uniqueness Problems, Journal of Function Spaces, 2016, 2016, 1  crossref(new windwow)
 References
1.
S. Bank and I. Laine, On the oscillation theory of f" + A(z)f = 0 where A is entire, Trans. Amer. Math. Soc. 273 (1982), no. 1, 351-363.

2.
P. D. Barry, On a theorem of Besicovitch, Quart. J. Math. Oxford Ser. (2) 14 (1963), 293-320. crossref(new window)

3.
R. Bruck, On entire functions which share one value CM with their first derivatives, Results Math. 30 (1996), no. 1-2, 21-24. crossref(new window)

4.
A. Chen, F. Lu, and H. X. Yi, Value sharing of meromorphic functions and their derivatives, J. Math. Anal. Appl. 359 (2009), no. 2, 696-703. crossref(new window)

5.
Z. X. Chen and Z. L. Zhang, Entire functions sharing fixed points with their higher order derivatives, Acta Math. Sinica (Chin. Ser.) 50 (2007), no. 6, 1213-1222.

6.
J. Grahl and C. Meng, Entire functions sharing a polynomial with their derivatives and normal families, Analysis (Munich) 28 (2008), no. 1, 51-61.

7.
I. Laine, Nevanlinna Theory and Complex Differential Equations, de Gruyter Studies in Mathematics, 15. Walter de Gruyter & Co., Berlin, 1993.

8.
X. M. Li and C. C. Gao, Entire functions sharing one polynomial with their derivatives, Proc. Indian Acad. Sci. Math. Sci. 118 (2008), no. 1, 13-26. crossref(new window)

9.
X. J. Liu, S. Nevo, and X. C. Pang, On the kth derivative of meromorphic functions with zeros of multiplicity at least k+1, J. Math. Anal. Appl. 348 (2008), no. 1, 516-529. crossref(new window)

10.
F. Lu, J. F. Xu, and A. Chen, Entire functions sharing polynomials with their first derivatives, Arch. Math. (Basel) 92 (2009), no. 6, 593-601. crossref(new window)

11.
F. Lu and H. X. Yi, On the uniqueness problems of meromorphic functions and their linear differential polynomials, J. Math. Anal. Appl. 362 (2010), no. 2, 301-312. crossref(new window)

12.
H. X. Yi and C. C. Yang, Uniqueness Theory of Meromorphic Functions, Science Press, Beijing, 1995.

13.
J. Zhang and L. W. Liao, On Bruck's conjecture on entire functions sharing one value with their derivatives, Houston. J. Math. 36 (2010), no. 2, 665-674.