Results on uniqueness of meromorphic functions of differential polynomial

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DOI:

https://doi.org/10.26637/MJM0601/0002

Abstract

In this paper, we study the problem concerning meromorphic functions sharing a small function with weight $l \geq 0$ and present one theorem which extends a results due to Zhang and Lü [19], S.S. Bhoosnurmath and Kabbur [5], Banerjee and Majumder [3], K. S. Charak and Banarsi Lal [7].

Keywords:

Uniqueness, Meromorphic function, Sharing values, Differential Polynomial, Weighted sharing

Mathematics Subject Classification:

Mathematics
  • Harina P. Waghamore Department of Mathematics, Jnanabharathi Campus, Bangalore University, Bengaluru-560056, India.
  • Naveenkumar S. H. Department of Mathematics, Jnanabharathi Campus, Bangalore University, Bengaluru-560056, India.
  • Pages: 14-20
  • Date Published: 01-01-2018
  • Vol. 6 No. 01 (2018): Malaya Journal of Matematik (MJM)

Banerjee, Abhijit. Meromorphic functions sharing one value. Int. J. Math. Math. Sci. 2005, no. 22, 3587-3598.

Banerjee, Abhijit; Majumder, Sujoy. On the uniqueness of a power of a meromorphic function sharing a small function with the power of its derivative. Comment. Math. Univ. Carolin. 51 (2010), no. 4, 565-576.

Banerjee, Abhijit; Majumder, Sujoy. Some uniqueness results related to meromorphic function that share a small function with its derivative. Math. Rep. (Bucur.) 16(66) (2014), no. 1, 95-111.

Banerjee, Abhijit; Chakraborty, Bikash. Further investigations on a question of Zhang and Lü. Ann. Univ. Paedagog. Crac. Stud. Math. 14 (2015), 105-119.

Bhoosnurmath, Subhas S.; Kabbur, Smita R. On entire and meromorphic functions that share one small function with their differential polynomial. Int. J. Anal. 2013, Art. ID $926340,8 mathrm{pp}$.

Bhoosnurmath, S. S.; Patil, Anupama J. On the growth and value distribution of meromorphic functions and their differential polynomials. J. Indian Math. Soc. (N.S.) 74 (2007), no. 3-4, 167-184 (2008).

Kuldeep Singh Charak; Banarsi Lal. Uniqueness of $f^n$ and $P[f]$, arXiv:1501.05092v1.[math.CV]21 Jan 2015.

Harina P. Waghamore.; Rajeshwari S. Weighted value sharing and uniqueness of entire and meromorphic functions. Malaya Journal of Matematik. 5(3)(2017), 540-549.

Hayman, W. K. Meromorphic functions. Oxford Mathematical Monographs Clarendon Press, Oxford 1964 xiv+191 pp.

Huang, Hui; Huang, Bin. Uniqueness of meromorphic functions concerning differential monomials. Appl. Math. (Irvine) 2 (2011), no. 2, 230-235.

Lahiri, Indrajit; Sarkar, Arindam. Uniqueness of a meromorphic function and its derivative. JIPAM. J. Inequal. Pure Appl. Math. 5 (2004), no. 1, Article 20, 9 pp. (electronic).

Li, Nan; Yang, Lian-Zhong. Meromorphic function that shares one small function with its differential polynomial. Kyungpook Math. J. 50 (2010), no. 3, 447-454.

Li, Jin-Dong; Huang, Guang-Xin. On meromorphic functions that share one small function with their derivatives. Palest. J. Math. 4 (2015), no. 1, 91-96.

Mues, Erwin; Steinmetz, Norbert. Meromorphe Funktionen, die mit ihrer Ableitung Werte teilen. (German) Manuscripta Math. 29 (1979), no. 2-4, 195-206.

Yang, Chung-Chun; Yi, Hong-Xun. Uniqueness theory of meromorphic functions. Mathematics and its Applications, 557. Kluwer Academic Publishers Group, Dordrecht, 2003. viii+569 pp. ISBN: 1-4020-1448-1.

Yi, Hong Xun. Uniqueness of meromorphic functions and a question of C. C. Yang. Complex Var. Theory and Appl. 14 (1990), no. 1-4, 169-176.

Yi, Hong-Xun. Uniqueness theorems for meromorphic functions whose $n$th derivatives share the same 1-points. Complex Var. Theory and Appl. 34 (1997), no. 4, 421436.

Zhang, Qing Cai. The uniqueness of meromorphic functions with their derivatives. Kodai Math. J. 21 (1998), no. 2, 179-184.

Zhang, Tongdui; Lü, Weiran. Notes on a meromorphic function sharing one small function with its derivative. Complex Var. Elliptic Equ. 53 (2008), no. 9, 857-867.

Q.C.Zhang. Meromorphic function that shares one small function with its derivative. J.Inequal.Pure.Appl.Math.,6(2015),1-13.

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Published

01-01-2018

How to Cite

Harina P. Waghamore, and Naveenkumar S. H. “Results on Uniqueness of Meromorphic Functions of Differential Polynomial”. Malaya Journal of Matematik, vol. 6, no. 01, Jan. 2018, pp. 14-20, doi:10.26637/MJM0601/0002.