Nonlinear differential polynomial sharing a nonzero polynomial with certain degree
Dedicated to Professor Ioan A. Rus on the occasion of his 80th anniversary
Keywords:
Uniqueness, meromorphic function, weighted sharing, non-linear differential polynomials.Abstract
In this paper we study the uniqueness problems of meromorphic functions when certain non-linear dierential polynomial sharing a nonzero polynomial with certain degree. We obtain some results which will rectify, improve and generalize some recent results of C. Wu and J. Li [15] in a large extent. Our results will also improve and generalize some recent results due to Fang [5], Zhang-Zhang [24], Zhang [22], Xu et al. [16], Qi-Yang [14], Dou-Qi-Yang [4], Zhang-Xu [26] and Liu-Yang [13].
Mathematics Subject Classification (2010): 30D35.
References
Alzahary, T.C., Yi, H.X., Weighted value sharing and a question of I. Lahiri, Complex Var. Theory Appl., 49(2004), no. 15, 1063-1078.
Banerjee, A., Meromorphic functions sharing one value, Int. J. Math. Math. Sci., 22(2005), 3587-3598.
Chen, H.H., Yoshida functions and Picad values of integral functions and their derivatives, Bull. Aust. Mat. Soc., 54(1996), 373-381.
Dou, J., Qi, X.G., Yang, L.Z., Entire functions that share fixed points, Bull. Malays. Math., 34(2011), no. 2, 355-367.
Fang, M.L., Uniqueness and value-sharing of entire functions, Comput. Math. Appl., 44(2002), 823-831.
Frank, G., Eine Vermutung Von Hayman uber Nullslellen meromorphic Funktion, Math. Z., 149(1976), 29-36.
Hayman, W.K., Meromorphic Functions, The Clarendon Press, Oxford, 1964.
Lahiri, I., Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J., 161(2001), 193-206.
Lahiri, I., Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl., 46(2001), 241-253.
Lahiri, I., Dewan, S., Value distribution of the product of a meromorphic function and its derivative, Kodai Math. J., 26(2003), 95-100.
Lahiri, I., Sarkar, A., Nonlinear differential polynomials sharing 1-points with weight two, Chinese J. Contemp. Math., 25(2004), no. 3, 325-334.
Li, P., Yang, C.C., On the characteristics of meromorphic functions that share three values CM, J. Math. Anal. Appl., 220(1998), 132-145.
Liu, Y., Yang, L.Z., Some Further Results On Uniqueness Of Entire Functions And Fixed Points, Kyungpook. Math. J., 53(2013), 371-383.
Qi, X.G., Yang, L.Z., Uniqueness of entire functions and fi xed points, An. Polon. Math., 97(2010), 87-100.
Wu, C., Li, J., Uniqueness of meromorphic functions sharing a value, Vietnam J. Math., 41(2013), 289-302.
Xu, J.F., Lu, F., Yi, H.X., Fixed points and uniqueness of meromorphic functions, Comput. Math. Appl., 59(2010), 9-17.
Yang, C.C., On defi ciencies of differential polynomials II, Math. Z., 125(1972), 107-112.
Yamanoi, K., The second main theorem for small functions and related problems, Acta Math., 192(2004), 225-294.
Yi, H.X., On characteristic function of a meromorphic function and its derivative, Indian J. Math., 33(1991), no. 2, 119-133.
Yi, H.X., Meromorphic functions that share one or two values II, Kodai Math. J., 22(1999), 264-272.
Yang, C.C., Yi, H.X., Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers, Dordrecht/Boston/London, 2003.
Zhang, J.L., Uniqueness theorems for entire functions concerning fi xed-points, Comput. Math. Appl., 56(2008), 3079-3087.
Zhang, Q.C., Meromorphic function that shares one small function with its derivative, J. Inequal. Pure Appl. Math., 6(2005), no. 4, Art. 116 [ONLINE http://jipam.vu.edu.au/].
Zhang, J.F., Zhang, X.Y., Uniqueness of entire fu nctions that share one value, Comput. Math. Appl., 56(2008), 3000-3014.
Zhang, X., Xu, J., Yi, H., Value sharing of meromorphic functions and Fang's problem, arXiv: 1009.2132v1 [math.CV].
Zhang, X.B., Xu, J.F., Uniqueness of meromorphic functions sharing a small function and its applications, Comput. Math. Appl., 61(2011), 722-730.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2016 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.