On the Uniqueness of Certain Type of Difference Polynomial Sharing a Small Function
DOI:
https://doi.org/10.18311/jims/2018/18898Keywords:
Meromorphic Function, Difference Polynomial, Uniqueness.Abstract
The purpose of this paper is to study the uniqueness problems of certain type of difference polynomial sharing a small function. In this paper, we not only point out some gaps in the proof of the main results in [14], but also rectify the errors and present our main results in a more compact way. Also we exhibit two examples to show that one of the conditions of our result is the best possible.Downloads
Metrics
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2018 Sujoy Majumder, Somnath Saha
This work is licensed under a Creative Commons Attribution 4.0 International License.
Accepted 2018-01-02
Published 2018-01-04
References
A. Banerjee and S. Mukherjee, Uniqueness of meromorphic functions concerning differential monomials sharing the same value, Bull. Math. Soc. Sci. Math. Roumanie (N.S), 50 (2007), 191-206.
W. Bergweiler and A. Eremenko, On the singularities of the inverse to a meromorphic function of nite order, Rev. Mat. Iberoam, 11 (1995), 355-373.
Y. M. Chiang and S. J. Feng, On the Nevanlinna characteristic f(z +f) and difference equations in complex plane, Ramanujan J., 16 (2008), 105-129.
W. K. Hayman, Picard values of meromorphic Functions and their derivatives, Ann. of Math., 70 (1959), 9-42.
W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford (1964).
J. Heittokangas, R. Korhonen, I. Laine, J. Rieppo and J. L. Zhang, Value sharing results for shifts of meromorphic function, and sufficient conditions for periodicity, J. Math. Anal. Appl., 355 (2009), 352-363.
I. Lahiri, Value distribution of certain differential polynomials, Int. J. Math. Math. Sc., 28 (2001), 83-91.
I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl., 46 (2001), 241-253.
I. Laine and C. C. Yang, Value distribution of difference polynomials, Proc. Japan Acad. Ser. A, 83 (2007), 148-151.
S. Lin and W. C. Lin, Uniqueness of meromorphic functions concerning weakly weighted sharing, Kodai Math. J., 29 (2006), 269-280.
K. Liu and L. Z. Yang, Value distribution of the difference operator, Arch. Math. 92 (2009), 270-278.
C. Meng, Uniqueness of entire functions concerning difference polynomials, Math. Bohem., 139 (2014), 89-97.
E. Mues, Uber ein problem von Hayman, Math Z., 164 (1979), 239-259.
P. Sahoo and H. Karmakar, Results on uniqueness of entire functions whose certain difference polynomials share a small function, Analysis Mathematica, 41 (2015), 257272.
X. G. Qi, L. Z. Yang and K. Liu, Uniqueness and periodicity of meromorphic functions concerning the difference operator, Comput. Math. Appl, 60 (2010), 1739-1746.
K. Yamanoi, The second main theorem for small functions and related problems, Acta Math., 192 (2004) 225-294.
C. C. Yang, On deciencies of differential polynomials II, Math. Z., 125 (1972), 107-112.
J. L. Zhang, Value distribution and shared sets of differences of meromorphic functions, J. Math. Anal. Appl., 367 (2010), 401-408.
Q. C. Zhang, Meromorphic function that shares one small function with its derivative, J. Inequal. Pure Appl. Math., 6 (4) (2005), Art.116 [ ONLINE http://jipam.vu.edu.au/].