Acknowledgement
Supported by : Education Department of Liaoning Province, Shenyang Aerospace University
References
- A. Al-Khaladi, On meromorphic functions that share one value with their derivative, Analysis 25(2005), 131-140. https://doi.org/10.1515/anly-2005-0204
- A. Banerjee, Uniqueness of meromorphic functions that share two sets, Southeast Asian Bull. Math. 31(2007), 7-17.
- D.C. Barnett, R.G. Halburd, R.J. Korhonen and W. Morgan, Nevanlinna theory for the q-difference operator and meromorphic solutions of q-difference equations, Proc. Roy. Soc. Edinburgh Sect. A 137(2007), 457-474. https://doi.org/10.1017/S0308210506000102
- R. Bruck, On entire functions which share one value CM with their first derivative, Results Math. 30(1996), 21-24. https://doi.org/10.1007/BF03322176
- J.M. Chang and Y.Z. Zhu, Entire functions that share a small function with their derivatives, J. Math. Anal. Appl. 351(2009), 491-496. https://doi.org/10.1016/j.jmaa.2008.07.080
- Z.X. Chen, On the difference counterpart of Bruck conjecture, Acta Math. Sci. 34(2014), 653-659. https://doi.org/10.1016/S0252-9602(14)60037-0
- Z.X. Chen and K.H. Shon, On conjecture of R. Bruck concerning the entire function sharing one value CM with its derivatives, Taiwanese J. Math. 8(2004), 235-244. https://doi.org/10.11650/twjm/1500407625
- Z.X. Chen and H.X. Yi, On sharing values of meromorphic functions and their differences, Results Math. 63(2013), 557-565. . https://doi.org/10.1007/s00025-011-0217-7
-
Y.M. Chiang and S.J. Feng, On the Nevanlinna characteristic of f(z +
$\eta$ ) and difference equations in the complex plane, Ramanujan J. 16(2008), 105-129. https://doi.org/10.1007/s11139-007-9101-1 - X.J. Dong and K. Liu,Some results on differential-difference analogues of Bruck conjecture, Math. Slovaca 67(2017), 691-700. https://doi.org/10.1515/ms-2017-0002
- J. Grahl and C. Meng, Entire functions sharing a polynomial with their derivatives and normal families, Analysis 28(2008), 51-61. https://doi.org/10.1524/anly.2008.0902
- G.G. Gundersen and L.Z. Yang, Entire functions that share one value with one or two of their derivatives, J. Math. Anal. Appl. 223(1998), 88-95. https://doi.org/10.1006/jmaa.1998.5959
- R.G. Halburd and R.J. Korhonen, Nevanlinna theory for the difference operator, Ann. Acad. Sci. Fenn. Math. 31(2006), 463-478.
- W.K. Hayman, Meromorphic Functions, Clarendon, Oxford, 1964.
- J. Heittokangas, R.J. Korhonen, R. Laine, I. Rieppo and J.L. Zhang, Value sharing results for shifts of meromorphic functions and sucient conditions for periodicity, J. Math. Anal. Appl. 355(2009), 352-363. https://doi.org/10.1016/j.jmaa.2009.01.053
- I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J. 161(2001), 193-206. https://doi.org/10.1017/S0027763000027215
- I. Lahiri, Uniqueness of a meromorphic function and its derivative, J. Inequal. Pure Appl. Math. 5(1)(2004), Art. 20.
- P. Li, Entire functions that share one value with their linear differential polynomials, Kodai Math. J. 22(1999) 446-457. https://doi.org/10.2996/kmj/1138044096
- S. Li and Z.S. Gao, Entire functions sharing one or two finite values CM with their shifts or difference operators, Arch. Math. 97(2011), 475-483. https://doi.org/10.1007/s00013-011-0324-4
- X.M. Li, C.Y. Kang, H.X. Yi, Uniqueness theorems for entire functions sharing a nonzero complex number with their difference operators, Arch. Math. 96(2011), 577-587. https://doi.org/10.1007/s00013-011-0228-3
- X.M. Li, H.X. Yi and C.Y. Kang, Notes on entire functions sharing an entire function of a smaller order with their difference operators, Arch. Math. 99(2012), 261-270. https://doi.org/10.1007/s00013-012-0425-8
- K. Liu and X.J. Dong, Some results related to complex differential-dierence equations of certain types, Bull. Korean Math. Soc. 51(2014), 1453-1467. https://doi.org/10.4134/BKMS.2014.51.5.1453
- L.P. Liu and Y.X. Gu, Uniqueness of meromorphic functions that share one small function with their derivatives, Kodai Math. J. 27(2004), 272-279. https://doi.org/10.2996/kmj/1104247351
- F. Lu, J.F. Xu and H.X. Yi, Entire functions that share one value with their linear differential polynomials, J. Math. Anal. Appl. 342(2008) 615-628. https://doi.org/10.1016/j.jmaa.2007.12.045
- F. Lu and H.X. Yi, The Bruck conjecture and entire functions sharing polynomials with their k-th derivatives, J. Korean Math. Soc. 48(2011), 499-512. https://doi.org/10.4134/JKMS.2011.48.3.499
- C. Meng, On unicity of meromorphic function and its kth order derivative, J. Math. Inequal. 4(2010), 151-159. https://doi.org/10.7153/jmi-04-15
- D.C. Pramanik, M. Biswas and R. Mandal, On the study of Bruck conjecture and some non-linear complex differential equations, Arab J. Math. Sci. 23(2017), 196-204. https://doi.org/10.1016/j.ajmsc.2016.10.001
- X.G. Qi, N. Li and L.Z. Yang, Uniqueness of meromorphic functions concerning their dierences and solutions of dierence painleve equations, Comput. Methods Funct. Theory. 18(2018), 567-582. https://doi.org/10.1007/s40315-018-0241-7
- X.G. Qi and K. Liu, Uniqueness and value distribution of dierences of entire functions, J. Math. Anal. Appl. 379(2011), 180-187. https://doi.org/10.1016/j.jmaa.2010.12.031
- L.A. Rubel and C.C. Yang, Values shared by an entire function and its derivatives, In: Complex Analysis, Kentucky 1976 (Proc. Conf), Lecture Notes in Mathematics 599, Springer-Verlag, Berlin, 1977, 101-103.
- J.P. Wang, Entire functions that share a polynomial with one of their derivatives, Kodai Math. J. 27(2004), 144-151. https://doi.org/10.2996/kmj/1093351321
- J.P. Wang and H.X. Yi, Entire functions that share one value CM with their derivatives, J. Math. Anal. Appl. 277(2003) 155-163. https://doi.org/10.1016/S0022-247X(02)00526-7
- C.C. Yang, On deciencies of dierential polynomials, Math. Z. 125(1972), 107-112. https://doi.org/10.1007/BF01110921
- L.Z. Yang, Solution of a dierential equation and its applications, Kodai Math. J. 22(1999), 458-464. https://doi.org/10.2996/kmj/1138044097
- L.Z. Yang, Further results on entire functions that share one value with their derivatives, J. Math. Anal. Appl. 212(1997) 529-536. https://doi.org/10.1006/jmaa.1997.5528
- L. Yang, Value distribution theory, Springer-Verlag, Berlin, 1993.
- K.W. Yu, On entire and meromorphic functions that share small functions with their derivatives, J. Inequal. Pure Appl. Math. 4(1)(2003), Art. 21.
- J. Zhang and L.W. Liao, Entire functions sharing some values with their dierence operators, Sci. China Math. 57(2014), 2143-2152. https://doi.org/10.1007/s11425-014-4848-5
- J.L. Zhang, Meromorphic functions sharing a small function with their derivatives, Kyungpook Math. J. 49(2009), 143-154. https://doi.org/10.5666/KMJ.2009.49.1.143
- J.L. Zhang and R.J. Korhonen, On the Nevanlinna characteristic of f(qz) and its applications, J. Math. Anal. Appl. 369(2010), 537-544. https://doi.org/10.1016/j.jmaa.2010.03.038
- J.L. Zhang and L.Z. Yang, A power of a meromorphic function sharing a small function with its derivative, Ann. Acad. Sci. Fenn. Math. 34(2009), 249-260.
- J.L. Zhang and L.Z. Yang, A power of an entire function sharing one value with its derivative, Comput. Math. Appl. 60(2010), 2153-2160. https://doi.org/10.1016/j.camwa.2010.08.001
- J.L. Zhang and L.Z. Yang, Some results related to a conjecture of R. Bruck, J. Inequal. Pure Appl. Math. 8(1)(2007), Art. 18.
- Q.C. Zhang, Meromorphic function that share one small function with its derivative, J. Inequal. Pure Appl. Math. 6(4)(2005), Art. 116.