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http://dx.doi.org/10.4134/CKMS.c180378

A NOTE ON THE VALUE DISTRIBUTION OF DIFFERENTIAL POLYNOMIALS  

Bhoosnurmath, Subhas S. (Department of Mathematics Karnatak University)
Chakraborty, Bikash (Department of Mathematics Ramakrishna Mission Vivekananda Centenary College)
Srivastava, Hari M. (Department of Mathematics and Statistics University of Victoria)
Publication Information
Communications of the Korean Mathematical Society / v.34, no.4, 2019 , pp. 1145-1155 More about this Journal
Abstract
Let f be a transcendental meromorphic function, defined in the complex plane $\mathbb{C}$. In this paper, we give a quantitative estimations of the characteristic function T(r, f) in terms of the counting function of a homogeneous differential polynomial generated by f. Our result improves and generalizes some recent results.
Keywords
transcendental meromorphic function; differential polynomials;
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  • Reference
1 B. Chakraborty, Some ineuqlities related to dfferential monomials, arXiv:1802.03371v2 [math.CV] 5 Dec 2018.
2 W. K. Hayman, Meromorphic Functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964.
3 X. Huang and Y. Gu, On the value distribution of $f^2f^-(k)}$, J. Aust. Math. Soc. 78 (2005), no. 1, 17-26. https://doi.org/10.1017/S1446788700015536   DOI
4 Y. Jiang and B. Huang, A note on the value distribution of $f^1(f^-(k)})^n$, Hiroshima Math. J. 46 (2016), no. 2, 135-147. http://projecteuclid.org/euclid.hmj/1471024945   DOI
5 K. Yamanoi, Zeros of higher derivatives of meromorphic functions in the complex plane, Proc. Lond. Math. Soc. (3) 106 (2013), no. 4, 703-780. https://doi.org/10.1112/plms/pds051   DOI
6 I. Lahiri and S. Dewan, Inequalities arising out of the value distribution of a differential monomial, JIPAM. J. Inequal. Pure Appl. Math. 4 (2003), no. 2, Article 27, 6 pp.
7 N. Li and L.-Z. Yang, Meromorphic function that shares one small function with its differential polynomial, Kyungpook Math. J. 50 (2010), no. 3, 447-454. https://doi.org/10.5666/KMJ.2010.50.3.447   DOI
8 E. Mues, Uber ein Problem von Hayman, Math. Z. 164 (1979), no. 3, 239-259. https://doi.org/10.1007/BF01182271   DOI
9 Q. D. Zhang, A growth theorem for meromorphic functions, J. Chengdu Inst. Meteor. 20 (1992), 12-20.