Abstract
In this paper, we consider uniqueness problems on entire functions that share a small periodic entire functions with their shifts and difference operators, we improve also some results due to B. Chen, Z. X. Chen and S. Li.
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Bergweiler, W., Langley, J.K.: Zeros of differences of meromorphic functions. Math. Proc. Camb. Philos. Soc. 142(1), 133-147 (2007)
Chen, B., Chen, Z.X., Li, S.: Uniqueness problems on entire functions and their difference operators or shifts. Abstr. Appl. Anal. 2012. Article ID 906893 (2012)
Chen, B., Li, S.: Uniqueness theorems on entire functions that share small functions with their difference operators. Adv. Diff. Equ. 2014, 311 (2014)
Chen, Z.X.: Complex differences and difference equations, mathematics monograph series 29. Science Press, Beijing (2014)
Chiang, Y.M., Feng, S.J.: On the Nevanlinna characteristic of $f\left( z+\eta \right)$ and difference equations in the complex plane. Ramanujan J. 16(1), 105-129 (2008)
Halburd, R.G., Korhonen, R.J.: Difference analogue of the lemma on the logarithmic derivative with applications to difference equations. J. Math. Anal. Appl. 314(2), 477-487 (2006)
Halburd, R.G., Korhonen, R.J.: Nevanlinna theory for the difference operator. Ann. Acad. Sci. Fenn. Math. 31(2), 463-478 (2006)
Hayman, W.K.: Meromorphic functions. Oxford Mathematical Monographs Clarendon Press, Oxford (1964)
Heittokangas, J., Korhonen, R., Laine, I., Rieppo, J., Zhang, J.: Value sharing results for shifts of meromorphic functions, and sufficient conditions for periodicity. J. Math. Anal. Appl. 355, 352-363 (2009)
Jank, G., Mues, E., Volkmann, L.: Meromorphe funktionen, die mit ihrer ersten und zweiten ableitung einen endlichen wert teilen. Complex Var. Theory Appl. 6(1), 51-71 (1986)
Laine, I.: Nevanlinna theory and complex differential equations, de Gruyter studies in mathematics, 15. Walter de Gruyter & Co., Berlin (1993)
Rubel, L.A., Yang, C.C.: Values shared by an entire function and its derivatives, lecture notes in math, vol. 599, pp. 101-103. Springer, Berlin (1977)
Qi, X.G., Yang, L.Z., Liu, K.: Uniqueness and periodicity of meromorphic functions concerning the difference operator. Comput. Math. Appl. 60, 1739-1746 (2010)
Yang, C.C., Yi, H.X.: Uniqueness theory of meromorphic functions, Mathematics and its Applications, 557. Kluwer Academic Publishers Group, Dordrecht (2003)
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The authors would like to thank the anonymous referee for his/her helpful remarks and suggestions to improve this article.
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Communicated by Ronen Peretz.
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El Farissi, A., Latreuch, Z. & Asiri, A. On the Uniqueness Theory of Entire Functions and Their Difference Operators. Complex Anal. Oper. Theory 10, 1317–1327 (2016). https://doi.org/10.1007/s11785-015-0514-3
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DOI: https://doi.org/10.1007/s11785-015-0514-3