Browse > Article
http://dx.doi.org/10.4134/CKMS.c170360

UNIQUENESS OF TWO DIFFERENTIAL POLYNOMIALS OF A MEROMORPHIC FUNCTION SHARING A SET  

Ahamed, Molla Basir (Department of Mathematics Kalipada Ghosh Tarai Mahavidyalaya)
Publication Information
Communications of the Korean Mathematical Society / v.33, no.4, 2018 , pp. 1181-1203 More about this Journal
Abstract
In this paper, we are mainly devoted to find out the general meromorphic solution of some specific type of differential equation. We have also answered an open question posed by Banerjee-Chakraborty [4] by extending their results in a large extent. We have provided an example showing that the conclusion of the results of Zhang-Yang [16] is not general true. Some examples have been exhibited to show that certain claims are true in our main result. Finally some questions have been posed for the future research in this direction.
Keywords
meromorphic function; differential polynomial; set sharing; uniqueness;
Citations & Related Records
연도 인용수 순위
  • Reference
1 T. C. Alzahary, Meromorphic functions with weighted sharing of one set, Kyungpook Math. J. 47 (2007), no. 1, 57-68.
2 A. Banerjee and M. B. Ahamed, Meromorphic function sharing a small function with its differential polynomial, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 54 (2015), no. 1, 33-45.
3 A. Banerjee and M. B. Ahamed, Rational function and differential polynomial of a meromorphic function sharing a small function, Bull. Transilvania Univ. Brasov., Series III, Math. Info. Phys., 59 (2017), no. 10, 1-18.
4 A. Banerjee and B. Chakraborty, Uniqueness of the power of meromorphic functions with its differential polynomial sharing a set, Math. Morav. 20 (2016), no. 2, 1-14.   DOI
5 W. K. Hayman, Meromorphic Functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964.
6 I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J. 161 (2001), 193-206.   DOI
7 I. Lahiri and A. Sarkar, Uniqueness of meromorphic function and its derivative, J. Inequal. Pure Appl. Math. 5 (2004), no. 1, Art.20 [ONLINE http://jipam.vu.edu.au/].
8 W.-C. Lin and H.-X. Yi, Uniqueness theorems for meromorphic functions that share three sets, Complex Var. Theory Appl. 48 (2003), no. 4, 315-327.
9 E. Mues and N. Steinmetz, Meromorphe Funktionen, die mit ihrer Ableitung Werte teilen, Manuscripta Math. 29 (1979), no. 2-4, 195-206.   DOI
10 A. Z. Mokhon'ko, On the Nevanlinna characteristics of some meromorphic functions, in "Theory of Functions, functional analysis and their applications", Izd-vo Khar'kovsk, Un-ta, 14 (1971), 83-87.
11 L. A. Rubel and C. C. Yang, Values shared by an entire function and its derivative, in Complex analysis (Proc. Conf., Univ. Kentucky, Lexington, Ky., 1976), 101-103. Lecture Notes in Math., 599, Springer, Berlin, 1977.
12 L.-Z. Yang and J.-L. Zhang, Non-existence of meromorphic solutions of a Fermat type functional equation, Aequationes Math. 76 (2008), no. 1-2, 140-150.   DOI
13 H. X. Yi, Uniqueness of meromorphic functions and a question of C. C. Yang, Complex Variables Theory Appl. 14 (1990), no. 1-4, 169-176.   DOI
14 H. X. Yi, Uniqueness theorems for meromorphic functions whose nth derivatives share the same 1-points, Complex Variables Theory Appl. 34 (1997), no. 4, 421-436.   DOI
15 H. X. Yi, Uniqueness theorems for meromorphic functions. II, Indian J. Pure Appl. Math. 28 (1997), no. 4, 509-519.
16 J. Zhang and L. Yang, A power of a meromorphic function sharing a small function with its derivative, Ann. Acad. Sci. Fenn. Math. 34 (2009), no. 1, 249-260.