Uniqueness of certain type of differential-difference and difference polyniminals

Main Article Content

Abhijit Banerjee
Sujoy Majumder


In this paper we consider certain difference and differential-difference polynomials sharing some polynomial and improve a number of results in \cite{8a}, \cite{8aa} and \cite{18}. In particular we point out a gap in the argument in the proof of the main results in \cite {8aa} and rectifying the same we improve and extend the result to a large extent.

Article Details

How to Cite
Banerjee, A., & Majumder, S. (2018). Uniqueness of certain type of differential-difference and difference polyniminals. Tamkang Journal of Mathematics, 49(1), 1–24. https://doi.org/10.5556/j.tkjm.49.2018.2234
Author Biographies

Abhijit Banerjee

Department ofMathematics, University of Kalyani,West Bengal 741235, India.

Sujoy Majumder

Department ofMathematics, Raiganj University, Raiganj,West Bengal-733134, India.


T. C. Alzahary and H. X. Yi, Weighted value sharing and a question of I. Lahiri, Complex Var. Theory Appl., 49 (15) (2004), 1063-1078.

A. Banerjee, Meromorphic functions sharing one value, Int. J. Math. Math. Sci., 22 (2005), 3587-3598.

Y. M. Chiang and S. J. Feng, On the Nevanlinna characteristic $f(z+eta)$ and difference equations in complex plane, Ramanujan J., 16 (2008), 105-129.

W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford (1964)


I. Lahiri, Value distribution of certain differential polynomials, Int. J. Math. Math. Sci., 28 (2001), 83-91.

I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J., 161 (2001), 193-206.

I. Lahiri and S. Dewan, Value distribution of the product of a meromorphic function and its derivative, Kodai Math. J., 26 (2003), 95-100.

I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl., 46 (2001), 241-253.

K. Liu, X. L. Liu and T. B. Cao, Some results on zeros and uniqueness of difference-differential polynomials, Appl. Math. J. Chinese Univ., 27 (1) (2012), 94-104.

X. G. Qi, L. Z. Yang and K. Liu, Uniqueness and periodicity of meromorphic functions concerning the difference operator, Com. Math. Appl., 60 (6) (2010), 1739-1746.

C. Wu, Uniqueness of entire functions concerning difference operator, Abstract and Applied Analysis, Vol. 2013, Art. Id 240369, 9 pages.

C. C. Yang, On deficiencies of differential polynomials II, Math. Z., 125 (1972), 107-112.

L. Yang, Value Distribution Theory, Springer-Verlag and Science Press, 1993.

C. C. Yang and H. X. Yi, Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers, Dordrecht/Boston/London, 2003.

K. Yamanoi, The second main theorem for small functions and related problems, Acta Math., 192 (2004), 225-294.

Q. C. Zhang, Meromorphic function that shares one small function with its derivative, J. Inequal. Pure Appl. Math., 6 (4) (2005), Art.116 http://jipam.vu.edu.au/].

J. L. Zhang, Z. S. Gao and S. Li, Distribution of zeros and shares values of difference operator, Annal. Polon. Math., 102 (3) (2011), 213-221.