Abstract
In this paper we investigate the possible relation between two meromorphic functions fn f(k) and gn g(k) that share a nonzero polynomial and obtain two results which are related to a conjecture of X. Y. Cao and B. X. Zhang [Uniqueness of meromorphic functions sharing two values, J. Ineq. Appl., 1(100) (2012)]
Acknowledgement
The author is grateful to the referee for his/her valuable comments and suggestions to-wards the improvement of the paper.
References
[1] Bergweiler, W.—Eremenko, A.: On the singularrities of the inverse to a meromorphic function of finite order, Rev. Mat. Iberoam. 11 (1995), 355– 373.10.4171/RMI/176Search in Google Scholar
[2] Chen, H. H.—Fang, M. L.: On the value distribution of fn f′, Sci. China Ser. A. 38 (1995), 789-798.Search in Google Scholar
[3] Cao, X. Y.—Zhang, B. X.: Uniqueness of meromorphic functions sharing two values, J. Ineq. Appl. 1 (2012).10.1186/1029-242X-2012-100Search in Google Scholar
[4] Fang, M. L.—Hua, X. H.: Entire functions that share one value, J. Nanjing Univ. Math. Biquarterly 13 (1996), 44-48.Search in Google Scholar
[5] Fang, M. L.—Qiu, H. L.: Meromorphic functions that share fixed-points, J. Math. Anal. Appl. 268 (2002), 426-439.10.1006/jmaa.2000.7270Search in Google Scholar
[6] Frank, G.: Eine Vermutung Von Hayman über Nullslellen meromorphic Funktion, Math. Z. 149 (1976), 29-36.10.1007/BF01301627Search in Google Scholar
[7] Hayman, W. K.: Meromorphic Functions, The Clarendon Press, Oxford 1964.Search in Google Scholar
[8] Lahiri, I.: Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J. 161 (2001), 193-206.10.1017/S0027763000027215Search in Google Scholar
[9] Lahiri, I.: Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theo. Appl. 46 (2001), 241-253.Search in Google Scholar
[10] Lahiri, I.—Dewan, S.: Value distribution of the product of a meromorphic function and its derivative, Kodai Math. J. 26 (2003), 95-100.Search in Google Scholar
[11] Lahiri, I.—Dewan, S.: Inequalities arising out of the value distribution of a differential monomial, J. Inequal. Pure Appl. Math. 4 (2003), Article 27.Search in Google Scholar
[12] Lahiri, I.—Sarkar, A.: Nonlinear differential polynomials sharing 1-points with weight two, Chinese J. Contemp. Math. 25 (2004), 325-334.Search in Google Scholar
[13] Li, X. M. and Cao, L.: Meromorphic functions sharing a nonzero polynomial CM, Bull. Korean Math. Soc. 47 (2010), 319-329.10.4134/BKMS.2010.47.2.319Search in Google Scholar
[14] Nevanlinna, R.: Einige Eindeutigkeitssätze in der Theorie der Meromorphen Funktionen, Acta Math. 48 (1926), 367-391.10.1007/BF02565342Search in Google Scholar
[15] Yamanoi, K.: The second main theorem for small functions and related problems, Acta Math. 192 (2004), 225-294.10.1007/BF02392741Search in Google Scholar
[16] Xu, J. F.—Yi, H. X.—Zhang, Z. L.: Some inequalities of differential polynomials, Math. Inequal. Appl. 12 (2009), 99-113.Search in Google Scholar
[17] Yang, C. C: On deficiencies of differential polynomials II, Math. Z. 125 (1972), 107-112.10.1007/BF01110921Search in Google Scholar
[18] Yang, C. C.—Hua, X. H.: Uniqueness and value-sharing of meromorphic functions, Ann. Acad. Sci. Fenn. Math. 22 (1997), 395-406.Search in Google Scholar
[19] Yi, H. X.: On characteristic function of a meromorphic function and its derivative, Indian J. Math. 33 (1991), 119-133.Search in Google Scholar
[20] Yi, H. X.—Yang, C. C: Uniqueness Theory of meromorphic functions, Science Press, Beijing, 1995.Search in Google Scholar
[21] Zhang, Z. L.—Li, W.: Picard exceptional values for two class differential polynomials, Acta Math. Sinica 34 (1994), 828-835.Search in Google Scholar
[22] Zhang, Q. C: Meromorphic function that shares one small function with its derivative, J. Inequal. Pure Appl. Math. 6 (2005), Art.116 [online http://jipam.vu.edu.au/].Search in Google Scholar
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