PDF(424 KB)
PDF(424 KB)
PDF(424 KB)
涉及导数与差分分担值的唯一性问题
Unicity of Mermorphic Functions Concerning Their Derivatives and Difference
本文研究了有穷级亚纯函数的导数及其差分分担值的唯一性问题，主要证明了以下结论：如果f'与Δcf CM分担a，b，∞，则f'≡Δcf.该结论解决了Qi等人在2018年提出的问题.
In this paper, we investigate a uniqueness of meromorphic functions with finite order concerning their derivative and difference and obtain one result that if f' and Δcf share a, b,∞ CM, then f' ≡ Δcf. This result confirms the problem of Qi et al. in 2018.
亚纯函数 / 差分 / 分担值 {{custom_keyword}} /
meromorphic function / difference / sharing value {{custom_keyword}} /
[1] Chen B. Q., Chen Z. X., Li S., Uniqueness theorems on entire functions and their difference operators or shifts, Abstr. Appl. Anal., 2012, 2012, Article ID 906893.
[2] Chen Z. X., Yi H. X., On sharing values of meromorphic functions and their differences, Result. Math., 2013, 63:557-565.
[3] Chiang Y. M., Feng S. J., On the Nevanlinna characteristic of f(z +η) and difference equations in the complex plane, Ramanujan J., 2008, 16(1):105-129.
[4] Cui N., Chen Z. X., The conjecture on unity of meromorphic functions concerning their differences, J. Difference Equ. Appl., 2016, 22(10):1452-1471.
[5] Halburd R. G., Korhonen R. J., Difference analogue of the lemma on the logarithmic derivative with applications to difference equations, J. Math. Anal. Appl., 2006, 314(2):477-487.
[6] Halburd R. G., Korhonen R. J., Nevanlinna theory for the difference operator, Ann. Acad. Sci. Fenn. Math., 2006, 31(2):463-478.
[7] Hayman W. K., Meromorphic Functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964.
[8] Heittokangas J., Korhonen R., Laine I., et al., Value sharing results for shifts of meromorphic function, and sufficient conditions for periodicity, J. Math. Anal. Appl., 2009, 355:352-363.
[9] Li X. M., Yi H. X., Yang C. C., Results on meromorphic functions sharing three values with their difference operators, Bull. Korean Math. Soc., 2015, 52(5):1401-1422.
[10] Liu D., Yang D. G., Fang M. L., Unicity of entire functions concerning shifts and difference operators, Abstr. Appl. Anal., 2014, 2014, Article ID 380910.
[11] Lü F., Lü W. R., Meromorphic functions sharing three values with their difference operators, Comput. Methods Funct. Theory, 2017, 17:395-403.
[12] Qi X. G., Li N., Yang L. Z., Uniqueness of meromorphic functions concerning their differences and solutions of difference Painlevé equations, Comput. Methods Funct. Theory, 2018, 18(4):567-582.
[13] Yang C. C., Yi H. X., Uniqueness Theory of Meromorphic Functions, Mathematics and Its Applications, 557, Kluwer Academic Publishers Group, Dordrecht, 2003.
[14] Ruble L. A., Yang C. C., Values shared by an entire function and its derivative, In:Comples Analysis (Proc. Com. Univ. Kentnchy), Vol. 599, 1977:101-103.
[15] Yang L., Value Distribution Theory, Springer-Verlag, Berlin, 1993.
[16] Zhang J., Liao L. W., Entire functions sharing some values with their difference operators, Sci. China Math., 2014, 57:2143-2152.
国家自然科学基金青年资助项目（11701188）
/
| 〈 |
|
〉 |
