On the periodicity of meromorphic functions when sharing two sets IM
DOI:
https://doi.org/10.24193/subbmath.2019.4.05Keywords:
Meromorphic function, shared sets, finite and infinite order, shift operator, periodicity.Abstract
In this paper, we have considered two sets sharing problems, and investigated on some sufficient conditions for the periodicity of meromorphic functions and obtained two results improving the result of Bhoosnurmath-Kabbur [6], Qi- Dou-Yang [17] and Zhang [20]. The results are: Let S1 = ( r z−a z : 0 (t − a)n(t − b)4dt + 1 = 0 and S2 = (a, b, where n ≥ 4(n ≥ 2) be an integer. Let f (z) be a non-constant meromorphic (entire) function satisfying Ef (z)(Sj ) = Ef (z+c)(Sj ), (j = 1, 2) then f (z) ≡ f (z + c). Some examples have been exhibited to show that, the meromorphic functions, we have considered may be of infinite order, and also to show that the sets considered in the main results, can’t be replace by some arbitrary sets. At the last section, we have posed a question for the future research in this direction.
Mathematics Subject Classification (2010): 30D35.
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