Result on uniqueness and weighted sharing of entire function of differential polynomial with their derivatives
Abstract
In this article, we worked on the uniqueness of more generalised form of a function namely \(f^{n}P(f)\) and \(\left[f^{n}P(f)\right]^{(k)}\) sharing a small function. The Theorem proved in this paper improves the results of Kit-wing [5].
2020 Mathematics Subject Classification:
30D35Keywords
entire function, uniqueness, small function, weighted sharing, differential polynomials
Author Details
S. H. Naveenkumar
Department of Mathematics
Bangalore Campus
GITAM University
Bengaluru-561203, India
e-mail: naveenkumarsh.220@gmail.com
References
- M. Fang, X. Hua. Entire functions that share one value. Journal of Nanjing University. Mathematical Biquarterly 13, 1 (1996), 44–48.
- W. K. Hayman. Meromorphic functions. Oxford Mathematical Monographs. Oxford, Oxford University Press, 1964, 191 pp.
- C.-C. Yang, H.-X. Yi. Uniqueness theory of meromorphic functions. Mathematics and its Applications, vol. 557. Dordrecht, Kluwer Academic Publishers Group, 2003, 569 pp.
- H.-X. Yi, C.-C. Yang. Uniqueness Theory of Meromorphic Functions. Science Press, Beijing, 1995.
- K.-W. Yu. On entire and meromorphic functions that share small functions with their derivatives. JIPAM. J. Inequal. Pure Appl. Math. 4, 1 (2003), Article 21, 7 pp.
- Q. C. Zhang. The uniqueness of meromorphic functions with their derivatives. Kodai Math. J. 21, 2 (1998), 179–184.