Acknowledgement
This work was financially supported by UGC India (F.16-6(DEC.2016)/2017(NET)).
References
- K. S. Charak, R. Korhonen, and G. Kumar, A note on partial sharing of values of meromorphic functions with their shifts, J. Math. Anal. Appl. 435 (2016), no. 2, 1241-1248. https://doi.org/10.1016/j.jmaa.2015.10.069
- S. Chen and W. C. Lin, Periodicity and uniqueness of meromorphic functions concerning sharing values, Houston J. Math. 43 (2017), no. 3, 763-781.
- Y.-M. Chiang and S.-J. Feng, On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane, Ramanujan J. 16 (2008), no. 1, 105-129. https://doi.org/10.1007/s11139-007-9101-1
- R. G. Halburd and R. Korhonen, Difference analogue of the lemma on the logarithmic derivative with applications to difference equations, J. Math. Anal. Appl. 314 (2006), no. 2, 477-487. https://doi.org/10.1016/j.jmaa.2005.04.010
- R. G. Halburd and R. Korhonen, Nevanlinna theory for the difference operator, Ann. Acad. Sci. Fenn. Math. 31 (2006), no. 2, 463-478.
- R. G. Halburd, R. Korhonen, and K. Tohge, Holomorphic curves with shift-invariant hyperplane preimages, Trans. Amer. Math. Soc. 366 (2014), no. 8, 4267-4298. https://doi.org/10.1090/S0002-9947-2014-05949-7
- W. K. Hayman, Meromorphic Functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964.
- J. Heittokangas, R. Korhonen, I. Laine, and J. Rieppo, Uniqueness of meromorphic functions sharing values with their shifts, Complex Var. Elliptic Equ. 56 (2011), no. 1-4, 81-92. https://doi.org/10.1080/17476930903394770
- J. Heittokangas, R. Korhonen, I. Laine, J. Rieppo, and J. Zhang, Value sharing results for shifts of meromorphic functions, and sufficient conditions for periodicity, J. Math. Anal. Appl. 355 (2009), no. 1, 352-363. https://doi.org/10.1016/j.jmaa.2009.01.053
- I. Laine, Nevanlinna theory and complex differential equations, De Gruyter Studies in Mathematics, 15, de Gruyter, Berlin, 1993. https://doi.org/10.1515/9783110863147
- P. Li, Unicity of meromorphic functions and their derivatives, J. Math. Anal. Appl. 285 (2003), no. 2, 651-665. https://doi.org/10.1016/S0022-247X(03)00459-1
- X. M. Li and H.-X. Yi, Meromorphic functions sharing four values with their difference operators or shifts, Bull. Korean Math. Soc. 53 (2016), no. 4, 1213-1235. https://doi.org/10.4134/BKMS.b150609
- C.-C. Yang and H.-X. Yi, Uniqueness theory of meromorphic functions, Mathematics and its Applications, 557, Kluwer Acad. Publ., Dordrecht, 2003.