Uniqueness of Meromorphic Functions Sharing a Certain Nonzero Polynomial With Weight
DOI:
https://doi.org/10.5644/SJM.12.1.04Keywords:
Uniqueness, meromorphic function, fixed point, non-linear differential polynomialsAbstract
In this paper we investigate the uniqueness problem of meromorphic functions when certain non-linear differential polynomials share a nonzero polynomial. We prove a uniqueness result which significantly rectify, improves and generalizes the recent results of P. Sahoo and S. Seikh as well as X. M. Li and L. Cao.
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References
M. L. Fang and H. L. Qiu, Meromorphic functions that share fixed points, J. Math. Anal. Appl., 268 (2002), 426–439.
G. Frank, Eine Vermutung Von Hayman uber ¨ Nullslellen meromorphic Funktion, Math. Z., 149 (1976), 29–36.
W. K. Hayman, Picard values of meromorphic Functions and their derivatives, Ann. Math., 70 (1959), 9–42.
W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford (1964).
I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J., 161 (2001), 193–206.
I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var., 46 (2001), 241–253.
I. Lahiri and A. Sarkar, Nonlinear differential polynomials sharing 1-points with weight two, Chinese J. Contemp. Math., 25 (3) (2004), 325–334.
I. Lahiri and S. Dewan, Value distribution of the product of a meromorphic function and its derivative, Kodai Math. J., 26 (2003), 95–100.
P. Li and C. C. Yang, On the characteristics of meromorphic functions that share three values CM, J. Math. Anal. Appl., 220 (1998), 132–145.
X. M. Li and L. Cao, Meromorphic functions sharing a nonzero polynomial CM, Bull. Korean Math. Soc., 47 (2010), 319–329.
W. C. Lin and H. X. Yi, Uniqueness theorems for meromorphic function, Indian J. Pure Appl. Math., 35 (2004), 121–132.
P. Sahoo and S. Seikh, Meromorphic functions sharing a nonzero polynomial with finite weight, Bull. Belg. Math. Soc. Simon Stevin, 20 (2013), 253–267.
J. F. Xu, F. L¨u and H. X. Yi, Fixed points and uniqueness of meromorphic functions, Comput. Math. Appl., 59 (2010), 9–17.
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.
K. Yamanoi, The second main theorem for small functions and related problems, Acta Math. 192 (2004), 225–294.
C. C. Yang and H. X. Yi, Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers, Dordrecht/Boston/London, 2003.
H. X. Yi, On characteristic function of a meromorphic function and its derivative, Indian J. Math., 33 (2) (1991), 119–133.
H. X. Yi, Meromorphic functions that share one or two values II, Kodai Math. J., 22 (1999), 264–272.
