Browse > Article
http://dx.doi.org/10.11568/kjm.2022.30.2.249

STUDY OF BRÜCK CONJECTURE AND UNIQUENESS OF RATIONAL FUNCTION AND DIFFERENTIAL POLYNOMIAL OF A MEROMORPHIC FUNCTION  

Pramanik, Dilip Chandra (Department of Mathematics, University of North Bengal)
Roy, Jayanta (Department of Mathematics, DDE,University of North Bengal)
Publication Information
Korean Journal of Mathematics / v.30, no.2, 2022 , pp. 249-261 More about this Journal
Abstract
Let f be a non-constant meromorphic function in the open complex plane ℂ. In this paper we prove under certain essential conditions that R(f) and P[f], rational function and differential polynomial of f respectively, share a small function of f and obtain a conclusion related to Brück conjecture. We give some examples in support to our result.
Keywords
Nevanlinna theory; Differential polynomial; Weighted sharing; Uniqueness;
Citations & Related Records
Times Cited By KSCI : 4  (Citation Analysis)
연도 인용수 순위
1 A. Z. Mohon's ko, On the Nevanlinna characterstics of some meromorphic functions, Theory of Functions. Functional Analysis and Their Applications 14 (1971), 83-87.
2 A. Banerjee and B. Chakraborty, On the generalizations of Bruck conjecture, Commun. Korean Math. Soc., 32 (2016), 311-327.
3 B. Chakraborty, Some uniqueness results related to the bruck conjecture, Analysis, 38(2) 2018, 91-100.   DOI
4 I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl. 46 (2001), 241-253.
5 N. Li, and L. Z. Yang, Meromorphic function that shares one small functions with its differential polynomial, Kyunpook Math. J. 50 (2010), 447-454.   DOI
6 L. Yang, Value distributions theory, Springer-Verlag, Berlin, (1993).
7 Hayman, W. K., Meromorphic function, Clarendon Press, Oxford, (1964).
8 I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J. 161 (2001), 193-206.   DOI
9 A. Banerjee and B. Chakraborty, Further investigations on a questions of Zhang and Lu, Ann. Univ. Paedagog. Crac. Stud. Math, 14 (2015), 105-119.   DOI
10 S. Bhoosnurmath and S. R. Kabbur, On entire and meromorphic functions that share one small function with their differential polynomial, Hindawi Publishing Corporation, Int. J. Analysis 2013, Article ID 926340.
11 J. L. Zhang and L. Z. Yang, Some result related to a conjecture of Bruck, J. Inequal. Pure. Appl. Math. 8 (2007), Art. 18.
12 I. Lahiri, Uniqueness of meromorphic functions and its derivatives, J. Inequal. Pure. Appl. Math. 5 (2004), Art. 20.
13 N. Li, L. Yang and K. Liu, A further result related to a conjecture of R. Bruck, Kyungpook. Math. J, 56 (2016), 451-464.   DOI
14 A. Chen and G. Zhang, Unicity of meromorphic function and its derivative, Kyungpook. Math. J, 50 (2010), 71-80.   DOI
15 K. S. Charak and B. Lal, Uniqueness of p(f) and P[f], Turk J Math. 40 (2016), 569-581.   DOI
16 B. Chakraborty, Uniqueness of power of a meromorphic function with its differential polynomial, Tamkang. J. Math., 50 (2019), 133-147.   DOI
17 H. X. Yi and C. C. Yang, Uniqueness theory of meromorphic functions(in Chinese), Science Press, Beijing, (1995).