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Uniqueness and periodicity of meromorphic functions concerning the difference operator. (English) Zbl 1202.30045
Summary: We investigate the uniqueness problems of difference polynomials of meromorphic functions that share a value or a fixed point. We also obtain several results concerning the shifts of meromorphic functions and the sufficient conditions for periodicity which improve some recent results of J. Heittokangas et al. [J. Math. Anal. Appl. 355, No. 1, 352–363 (2009; Zbl 1180.30039)] and K. Liu [J. Math. Anal. Appl. 359, No. 1, 384–393 (2009; Zbl 1177.30035)].

30D30General theory of meromorphic functions
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