Results on Certain Non-Linear Differential Polynomials Sharing a Small Function
Year 2014,
Volume: 5 , 17 - 34, 06.03.2015
Abhijit Banerjee
,
Molla Ahamed
Abstract
In the paper we shall mainly concern about the special types of non-linear dierential polynomial as introduced in [20] sharing a small function. Our main result will improve, extend, unify and generalize a number of recent results.
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- function with nite weight, Math. Vesnik., 65(2), (2013), 151-165.
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- -424.
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- -315.
- C.C.Yang and X.H.Hua, Uniqueness and value sharing of meromorphic functions,
- Ann.Acad.Sci.Fenn.Math. 22(1997), 395-406.
- H.X.Yi, On characteristic function of a meromorphic function and its derivative, Indian J. Math.
- (2)(1991), 119-133.
- H. X. Yi, C. C. Yang, Uniqueness Theory of meromorphic functions, Science Press, Beijing, 1995.
- K.Yamanoi, The second main theorem for small functions and related problems, Acta Math. 192(2004),
- -294.
- X. Y. Zhang, J. F. Chen and W.C. Lin, Entire or meromorphic functions sharing one value, Comput.
- Math. Appl. 56 (2008), 18761883.
- X. B. Zhang and J. F. Xu, Uniqueness of meromorphic functions sharing a small function and its
- applications, Comput. Math. Appl, 61(2011), 722-730.
- 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/].
Year 2014,
Volume: 5 , 17 - 34, 06.03.2015
Abhijit Banerjee
,
Molla Ahamed
References
- A. Banerjee and P. Bhattacharjee, Some uniqueness results related to certain nonlinear dierential poly-
- nomials sharing the same 1-points, Vietnam J. Math., 37 (2009), 97112.598.
- A.Banerjee, On uniqueness for non-linear dierential polynomials sharing the same 1-points, Ann. Polon.
- Math. 89(3) (2006), 259-272.
- A.Banerjee, A uniqueness result on some dierential polynomials sharing 1 points, Hiroshima Math. J.
- (3) 2007, 397-408.
- A.Banerjee and P.Sahoo, Uniqueness of meromorphic functions when two dierential polynomials share
- one value, Sarajevo.J. Math., 20(2012), 69-89
- M.L.Fang and W. Hong, A unicity theorem for entire functions concerning dierential polynomials, Indian
- J. Pure Appl. Math., 32(9) (2001), 1343-1348.
- W.K.Hayman, Meromorphic Functions, The Clarendon Press, Oxford (1964).
- I.Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J., 161 (2001), 193-
- -
- I.Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl.,
- (2001), 241-253.
- I. Lahiri and A. Banerjee, Weighted sharing of two sets, Kyungpook Math. J. Vol. 46 (2006) no. 1, pp.
- -87.
- I. Lahiri and S. Dewan, Value distribution of the product of a meromorphic function and its derivative,
- Kodai Math. J., 26(1) (2003), 95-100.
- I.Lahiri and N.Mandal, Uniqueness of nonlinear dierential polynomials sharing simple and double 1-
- points, Int. J. Math. Math. Sci. 12 (2005), 1933-1942.
- I.Lahiri and R.Pal, Nonlinear dierential polynomials sharing 1-points, Bull. Korean Math. Soc., 43(1)
- (2006), 161-168.
- I.Lahiri and A.Sarkar, Nonlinear dierential polynomials sharing 1-points with weight two, Chinese J.
- Contemp. Math., 25(3) (2004), 325-334.
- I.Lahiri and P.Sahoo, Uniqueness of non-linear dierential polynomials sharing 1-points, Georgian Math.
- J., 12(1) (2005), 131-138.
- W.C.Lin, Uniqueness of dierential polynomials and a question of Lahiri, Pure Appl. Math., 17(2)(2001),
- -110 (in Chinese).
- W.C.Lin and H.X.Yi, Uniqueness theorems for meromorphic function, Indian J. Pure Appl. Math.,
- (2)(2004), 121-132.
- C. Meng, On unicity of meromorphic functions when two dierential polynomials share one value, Hi-
- roshima Math. J., 39(2009), 163-169.
- C. Meng, Uniqueness for meromorphic functions concerning dierential polynomials, Georgian Math. J.,
- (4)(2008), 731-738.
- P. Sahoo and S. Seikh, Meromorphic functions whose certain dierential polynomials share a small
- function with nite weight, Math. Vesnik., 65(2), (2013), 151-165.
- S.H.Shen and W.C.Lin, Uniqueness of meromorphic functions, Complex Var. Elliptic Equ., 52(5)(2007),
- -424.
- W. L. Xiong, W. C. Lin and S. Mori, Uniqueness of meromorphic functions, Sci. Math. Jpn., 62(2) (2005),
- -315.
- C.C.Yang and X.H.Hua, Uniqueness and value sharing of meromorphic functions,
- Ann.Acad.Sci.Fenn.Math. 22(1997), 395-406.
- H.X.Yi, On characteristic function of a meromorphic function and its derivative, Indian J. Math.
- (2)(1991), 119-133.
- H. X. Yi, C. C. Yang, Uniqueness Theory of meromorphic functions, Science Press, Beijing, 1995.
- K.Yamanoi, The second main theorem for small functions and related problems, Acta Math. 192(2004),
- -294.
- X. Y. Zhang, J. F. Chen and W.C. Lin, Entire or meromorphic functions sharing one value, Comput.
- Math. Appl. 56 (2008), 18761883.
- X. B. Zhang and J. F. Xu, Uniqueness of meromorphic functions sharing a small function and its
- applications, Comput. Math. Appl, 61(2011), 722-730.
- 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/].