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Uniqueness of meromorphic function with its shift operator under the purview of two or three shared sets

  • Abhijit Banerjee EMAIL logo and Molla Basir Ahamed
Published/Copyright: May 21, 2019
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Abstract

Taking two and three shared set problems into background, the uniqueness problem of a meromorphic function together with its shift operator have been studied. Our results will improve a number of recent results in the literature. Some examples have been provided in the last section to show that certain conditions used in the paper, is the best possible.

MSC 2010: Primary 30D35
  1. (Communicated by Stanisława Kanas)

References

[1] Banerjee, A.: Some uniqueness results on meromorphic functions sharing three sets, Ann. Polon. Math. 92(3) (2007), 261–274.10.4064/ap92-3-5Search in Google Scholar

[2] Banerjee, A.—Bhattacharajee, P.: Uniqueness and set sharing of derivatives of meromorphic functions, Math. Slovaca 61(2) (2011), 197–214.10.2478/s12175-011-0005-6Search in Google Scholar

[3] Banerjee, A.—Mallick, S.: On the characterizations of the new class of strong uniqueness polynomials generating unique range sets, Comput. Math. Funct. Theo. 17 (2017), 19–45.10.1007/s40315-016-0174-ySearch in Google Scholar

[4] Bhoosnurmath, S. S.—Kabbur, S. R.: Value distribution and uniqueness theorems for difference of entire and meromorphic functions, Int. J. Anal. Appl. 2(2) (2013), 124–136.Search in Google Scholar

[5] Chen, B.—Chen, Z.: Meromorphic functions sharing two sets with its difference operator, Bull. Malays. Math. Soc. 35(3) (2012), 765–774.Search in Google Scholar

[6] Chen, B.—Chen, Z.—Li, S.: Uniqueness of difference operators of meromorphic functions, J. Inequal. Appl. 48 (2012), 1–19.10.1186/1029-242X-2012-48Search in Google Scholar

[7] Fujimoto, H.: On uniqueness of meromorphic functions sharing finite sets, Amer. J. Math. 122 (2000), 1175–1203.10.1007/978-1-4613-0269-8_34Search in Google Scholar

[8] Hayman, W. K.: Meromorphic Functions, The Clarendon Press, Oxford, 1964.Search in Google Scholar

[9] Lahiri, I.: Value distribution of certain differential polynomials, Int. J. Math. Math. Sci. 28(2) (2001), 83–91.10.1155/S0161171201011036Search in Google Scholar

[10] Lahiri, I.: Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J. 161 (2001), 193–206.10.1017/S0027763000027215Search in Google Scholar

[11] Lahiri, I.: Weighted value sharing and uniqueness of meromorphic functions, Complex Variables Theory and Application 46 (2001), 241–253.10.1080/17476930108815411Search in Google Scholar

[12] Mokhonko, A. Z.: On the Nevanlinna characteristics of some meromorphic functions, Funct. Anal. Appl. 14 (1971), 83–87.Search in Google Scholar

[13] Qi, X. G.—Dou J.—Yang, L. Z.: Uniqueness and value distribution for difference operator of meromorphic function, Adv. Difference Equ. 32 (2012), 1–9.10.1186/1687-1847-2012-32Search in Google Scholar

[14] Yi, H. X.: Meromorphic functions that share one or two values II, Kodai Math. J. 22 (1999), 264–272.10.2996/kmj/1138044046Search in Google Scholar

[15] Zhang, J. L.: Value distribution and sets of difference of meromorphic functions, J. Math. Anal. Appl. 367(2) (2010), 401–408.10.1016/j.jmaa.2010.01.038Search in Google Scholar

Received: 2017-10-15
Accepted: 2018-08-02
Published Online: 2019-05-21
Published in Print: 2019-06-26

© 2019 Mathematical Institute Slovak Academy of Sciences

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