Uniqueness of Meromorphic Functions When Two Differential Polynomials Share One Value
DOI:
https://doi.org/10.5644/SJM.08.1.05Keywords:
Meromorphic function, differential polynomial, weighted sharingAbstract
The paper deals with the uniqueness problems of meromorphic functions related to differential polynomials that share one value with finite weight. We prove three uniqueness results which significantly rectify, improve and supplement some recent results of [6] and [6b].
2000 Mathematics Subject Classification. 30D35
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References
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.
A. Banerjee, On uniqueness for non-linear differential polynomials sharing the same 1-point, Ann. Polon. Math., 89( 3) (2006), 259–272.
A. Banerjee and P. Bhattacharjee, Some uniqueness results related to certain nonlinear differential polynomials sharing the same 1-point, Vietnam J. Math., 37 (1) (2009), 97–112.
S. S. Bhoosnurmath and R. S. Dyavanal, Uniqueness and value sharing of meromorphic functions, Comput. Math. Appl., 53 (2007), 1191–1205.
R. S. Dyavanal, Uniqueness and value sharing of differential polynomials of meromorphic functions J. Math. Anal. Appl., 372 (1) (2010), 252–261.
R. S. Dyavanal, Erratum to uniqueness and value sharing of differential polynomials of meromorphic functions, J. Math. Anal. Appl., 374 (1) (2011), 334.
R. S. Dyavanal, Uniqueness and value sharing of differential polynomials of meromorphic functions, J. Math. Anal. Appl., 374 (1) (2011), 335–345.
C. Y. Fang and M. L. Fang, Uniqueness of meromorphic functions and differential polynomials, Comput. Math. Appl., 44 (2002), 607–617.
M. L. Fang and W. Hong, A unicity theorem for entire functions concerning differential polynomials, Indian J. Pure Appl. Math., 32 (2001), 1343–1348.
G. Frank and M. Reinders, A unique range set for meromorphic function with 11 elements, Complex Variables, 37 (1998), 185–193.
W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford (1964).
I. Lahiri, Uniqueness of meromorphic functions when two linear differential polynomials share the same 1-points, Ann. Polon. Math., 71 (1999), 113–128.
I. Lahiri, Value distribution of certain differential polynomials, Int. J. Math. Math. Sci., 28 (2) (2001), 83–91.
I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl., 46 (2001), 241–253.
I. Lahiri, Linear differential polynomials sharing the same 1-points with weight two, Ann. Polon. Math., 79 (2002), 157–170.
I. Lahiri, On a question of Hong Xun Yi, Arch. Math. (Brno), 38 (2002), 119–128.
I. Lahiri, Weighted sharing of three values, Z. Anal. Anwendungen, 23 (2)(2004), 237–252.
I. Lahiri and P. Sahoo, Uniqueness of meromorphic functions when two nonlinear differential polynomials share a small function, Arch. Math. (Brno), 44 (2008), 201–210.
W. C. Lin and H. X. Yi, Uniqueness theorems for meromorphic functions, Indian J. Pure Appl. Math., 35 (2004), 121–132.
C. C. Yang, On deficiencies of differential polynomials II, Math. Z., 125 (1972), 107–112.
C. C. Yang and X.H. Hua, Uniqueness and value sharing of meromorphic functions, Ann. Acad. Sci. Fenn. Math., 22 (1997), 395–406.
