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On the Uniqueness of Certain Type of Difference Polynomial Sharing a Small Function
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 , 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.
Meromorphic Function, Difference Polynomial, Uniqueness.
- 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/].
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