亚纯函数Milloux不等式的平移乘积及差分模拟
Analogues of Milloux Inequality of Meromorphic Functions Concerning Products of Shifts and Differences
DOI: 10.12677/PM.2020.1012139, PDF, HTML, 下载: 393  浏览: 563  国家自然科学基金支持
作者: 李可欣, 杨世伟, 杨德贵*:华南农业大学应用数学研究所,广东 广州
关键词: 亚纯函数Milloux不等式差分平移Meromorphic Functions Milloux Inequality Differences Shifts
摘要: 设f 是一个有穷级超越亚纯函数, 本文研究亚纯函数Milloux不等式的平移乘积及差分模拟, 获得 了涉及平移乘积及差分的Milloux不等式模拟. 对于所获得的涉及平移乘积的Milloux不等式模拟, 改进了吴昭君和徐洪等人近期的结果。
Abstract: Let f be a transcendental meromorphic function of finite order. In this paper, we stud- ied the analogues of Milloux Inequality of meromorphic functions concerning products of shifts and differences and obtained the analogues of Milloux Inequality of mero- morphic functions concerning products of shifts and differences. For the analogues of Miloux inequality concerning products of shifts, we improved the result of Wu and Xu.
文章引用:李可欣, 杨世伟, 杨德贵. 亚纯函数Milloux不等式的平移乘积及差分模拟[J]. 理论数学, 2020, 10(12): 1167-1175. https://doi.org/10.12677/PM.2020.1012139

参考文献

[1] Hayman, W.K. (1964) Meromorphic Functions. Clarendon Press, Oxford.
[2] Laine, I. (1993) Nevanlinna Theory and Complex Differential Equations. Walter de Gruyter, Berlin.
[3] Yang, L. (1993) Value Distribution Theory. Springer-Verlag, Berlin.
[4] Yang, C.C. and Yi, H.X. (2003) Uniqueness Theory of Meromoprhic Functions. Kluwer Aca- demic Publishers, Dordrecht, The Netherlands.
[5] Yi, H.X. (1989) Value Distribution of ftf . Chinese Science Bulletin, 34, 727-730.
https://doi.org/10.1360/csb1989-34-10-727
[6] Wu, Z.J. and Xu, H.Y. (2020) Milloux Inequality of Nonlinear Difference Monomials and Its Application. Journal of Mathematical Inequalities, 14, 819-827.
https://doi.org/10.7153/jmi-2020-14-52
[7] Halburd, R.G. and Korhonen, R.J. (2007) Meromorphic Solutions of Difference Equations, Integrability and the Discrete Painleve Equations. Journal of Physics A: Mathematical and Theoreticalis, 40, 1-38.
https://doi.org/10.1088/1751-8113/40/6/R01
[8] Halburd, R.G. and Korhonen, R.J. (2006) Nevanlinna Theory for the Difference Operator.Annales Academiæ Scientiarum Fennicæ, 31, 463-478.
[9] Chiang, Y.M. and Feng, S.J. (2009) On the Growth of Logarithmic Difference, Difference Equa- tions and Logarithmic Derivatives of Meromorphic Functions. Transactions of the American Mathematical Society, 361, 3767-3791.
https://doi.org/10.1090/S0002-9947-09-04663-7
[10] Halburd, R.G. and Korhonen, R.J. (2006) Difference Analogue of the Lemma on the Logarith- mic Derivative with Applications to Difference Equations. Journal of Mathematical Analysis and Applications, 314, 477-487.
https://doi.org/10.1016/j.jmaa.2005.04.010
[11] Chiang, Y.M. and Feng, S.J. (2008) On the Nevanlinna Characteristic of f (z+η) and Difference Equations in the Complex Plane. The Ramanujan Journal, 16, 105-129.
https://doi.org/10.1007/s11139-007-9101-1
[12] Zheng, R.R. and Chen, Z.X. (2012) Value Distribution of Difference Polynomials of Meromor- phic Functions. Science China Mathematics, 42, 1115-1130. (In Chinese)
https://doi.org/10.1360/012011-760