Uniqueness of power of ameromorphic functionwith its differential polynomial
In this paper, taking the question of Zhang and Lu into background,
we present one theorem which will improve and extend some recent
results related to Bruck Conjecture.
A. Banerjee, Uniqueness of meromorphic functions that share two sets, Southeast Asian Bull. Math., 31(1)(2007), 7–17.
A. Banerjee and B. Chakraborty, On the generalizations of Brück conjecture, Commun. Korean Math. Soc.,
(2) (2016), 311–327.
A. Banerjee and B. Chakraborty, Some further study on Brück conjecture, An. S¸tiin¸t. Univ. Al. I. Cuza Ia¸siMat.
(N.S.), 62(2) (vol. 2) (2016), 501–511.
A. Banerjee and B. Chakraborty, Further investigations on a question of Zhang and Lü, Ann. Univ. Paedagog.
Crac. Stud.Math., 14 (2015), 105–119.
B. Chakraborty, Some aspects of uniqueness theory of entire andmeromorphic functions, Ph.D. thesis, arXiv:
B. Chakraborty, Some uniqueness results related to the Brück conjecture, Analysis, 38(2) (2018), 91–100.
B. Chakraborty, A simple proof of the Chuang’s inequality, An. Univ. Vest Timis. Ser. Mat.-Inform., 55(2)
A. Banerjee and S.Majumder, On the uniqueness of a power of ameromorphic function sharing a small function
with the power of its derivative, Comment.Math. Univ. Carolin., 51(4) (2010), 565–576.
R. Brück, On entire functions which share one value CMwith their first derivative, ResultsMath., 30(1) (1996),
–24.UNIQUENESS OF AMEROMORPHIC FUNCTIONWITH ITS DIFFERENTIAL POLYNOMIAL 147
K. S. Charak and B. Lal, Uniqueness of f n and P[ f ], arXiv:1501.05092v1 [math.CV] 21 Jan 2015.
A. Chen and G. Zhang,Unicity ofmeromorphic function
and its derivative, KyungpookMath. J., 50(1) (2010),
C. T. Chuang, On differential polynomials, in: Analysis of one Complex Variable (Laramie 1985), World Scientific,
Singapore (1987), 12?2.
W. K. Hayman,Meromorphic Functions, The Clarendon Press, Oxford (1964).
I. Lahiri,Weighted value sharing and uniqueness ofmeromorphic functions, Complex Variables Theory Appl.,
I. Lahiri and A. Sarkar, Uniqueness of meromorphic function and its derivative, J. Inequal. Pure Appl. Math.,
(1) (2004), Article Id. 20.
J. D. Li and G. X. Huang, On meromorphic functions that share one small function with their derivatives,
Palestine J.Math., 4(1) (2015), 91–96.
N. Li and L. Z. Yang, Meromorphic function that shares one small function with its differential polynomial,
KyungpookMath. J., 50 (2010), 447-454.
N. Li, L. Z. Yang and K. Liu, A further result related to a conjecture of R. Brück, KyungpookMath. J., 56 (2016),
A. Z.Mokhon’ko, On the Nevanlinna characteristics of somemeromorphic functions, in Theory of Functions,
functional analysis and their applications, Izd-vo Khar’kovsk, Un-ta, 14 (1971), 83–87.
E.Mues andN. Steinmetz,Meromorphe Funktionen die unit ihrer AbleitungWerte teilen,ManuscriptaMath.,
L. A. Rubel and C. C. Yang, Values shared by an entire function and its derivative, Complex analysis (Proc.
Conf., Univ. Kentucky, Lexington, Ky., 1976), Lecture Notes inMath., 599 (1977), 101–103, Springer, Berlin.
Q. C. Zhang, The uniqueness ofmeromorphic functions with their derivatives, KodaiMath. J., 21 (1998), 179–
Q. C. Zhang, Meromorphic function that shares one small function with its derivative, J. Inequal. Pure Appl.
Math., 6(4) (2005), Article Id. 116.
T. D. Zhang and W. R. Lü, Notes on meromorphic function sharing one small function with its derivative,
Complex Var. Ellip. Eqn., 53(9) (2008), 857–867.