Open Access
Subscription Access
Open Access
Subscription Access
Unique Range Set of a Meromorphic Function And Its Linear Difference Polynomial
Subscribe/Renew Journal
In this work, we generalize the estimate of cardinality of a unique range set of meromorphic functions (URSM) and as an application we obtain the cardinality of URSM of a meromorphic function f(z) of finite order and its linear difference polynomial L(z, f). As a consequences we deduce several uniqueness of f(z) and L(z, f) sharing a set.
Keywords
Meromorphic Function; Linear Difference Polynomial; Finite Order; Unique Range Set; Nevanlinna Theory.
Subscription
Login to verify subscription
User
Font Size
Information
- A. Banerjee and B. Chakraborty, Further results on the uniqueness of meromorphic functions and their derivative counterpart sharing one or two sets, arXiv:1608.02539v1[math.CV](2016).
- W. Bergweiler and J. K. Langley, Zeros of differences of meromorphic functions, Math. Proc. Camb. Phil. Soc., 142 (2007), 133–147.
- S. S. Bhoosnurmath and S. R. Kabbur, Value distribution and uniqueness theorems for difference of entire and meromorphic functions, Int. J. Anal. Appl., 2 (2) (2013), 124–136.
- Y. M. Chiang and S. J. Feng, On the Nevanlinna characteristic of f(z + n) and the difference equations in the complex plane, Ramanunjan J., 16 (2008), 105–129.
- B. Chen and Z. Chen, Meromorphic functions sharing two sets with its difference operator, Bull. Malays. Math. Sci. Soc., Second Series, 35(3)) (2012), 765–774.
- G. Frank and M. Reinder, A unique range set for meromorphic functions with 11 elements, Comp. Vari. Theory Appl., 37 (1998), 185–193.
- R. G. Halburd and R. J. Korhonen, Nevanlinna theory for the difference operator, Anal. Acad. Sci. Fenn. Math., 31 (2), (2006), 463–478.
- I. Lahiri and A. Banerjee, Weighted sharing of two sets, Kyungpook Math. J., 46 (2006), 79–87.
- P. Li and C. C. Yang, Some further results on the unique range sets of meromorphic functions, Kodai Math. J., 18 (1995), 437–450.
- S. Li and B. Q. Chen, Unicity of meromorphic functions sharing sets with their linear difference polynomials, Abstr. Appl. Anal., Vol. 2014, Article ID 894968, 7 pages.
- X. Luo and W. C. Lin, Value sharing results for shifts of meromorphic functions, J. Math. Anal. Appl., 377 (2011), 441–449.
- C. C. Yang and H. X. Yi, Uniqueness Theory of Meromorphic Functions, Kluwer Academic, Dordrecht 2003.
- H. X. Yi, Unicity theorems for entire functions, Kodai Math. J., 17 (1994), 133–141.
- H. X. Yi and L. Z. Yang, Meromorphic functions that share two sets, Kodai Math. J., 20 (1997), 127–134.
- J. Zhang, Value distribution and shared sets of differences of meromorphic functions, J. Math. Anal. Appl., 367 (2) (2010), 4010–408.
Abstract Views: 135
PDF Views: 0