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Meromorphic functions sharing unique range sets with one or two elements

  • Jun-Fan Chen EMAIL logo

Abstract

The purpose of this paper is to study the problems of meromorphic functions sharing unique range sets with one or two elements, which can be seen as a new answer to a question due to Gross. The examples also illustrate the accuracy of all of the conditions.

MSC 2010: 30D35; 30D30

Award Identifier / Grant number: 2018J01658

Funding statement: The project was supported by the Natural Science Foundation of Fujian Province, China (Grant no. 2018J01658).

References

[1] J.-F. Chen, Uniqueness of meromorphic functions sharing two finite sets, Open Math. 15 (2017), no. 1, 1244–1250. 10.1515/math-2017-0102Search in Google Scholar

[2] J. B. Conway, Functions of one Complex Variable, Grad. Texts in Math. 11, Springer, New York, 1973. 10.1007/978-1-4615-9972-2Search in Google Scholar

[3] W. Doeringer, Exceptional values of differential polynomials, Pacific J. Math. 98 (1982), no. 1, 55–62. 10.2140/pjm.1982.98.55Search in Google Scholar

[4] M. Fang and W. Xu, On the uniqueness of entire functions, Bull. Malaysian Math. Soc. (2) 19 (1996), no. 1, 29–37. Search in Google Scholar

[5] M.-L. Fang and H. Guo, On meromorphic functions sharing two values, Analysis 17 (1997), no. 4, 355–366. 10.1524/anly.1997.17.4.355Search in Google Scholar

[6] G. Frank and M. Reinders, A unique range set for meromorphic functions with 11 elements, Complex Variables Theory Appl. 37 (1998), no. 1–4, 185–193. 10.1080/17476939808815132Search in Google Scholar

[7] H. Fujimoto, On uniqueness of meromorphic functions sharing finite sets, Amer. J. Math. 122 (2000), no. 6, 1175–1203. 10.1007/978-1-4613-0269-8_34Search in Google Scholar

[8] F. Gross, Factorization of meromorphic functions and some open problems, Complex Analysis (Lexington 1976), Lecture Notes in Math. 599, Springer, Berlin (1977), 51–67. 10.1007/BFb0096825Search in Google Scholar

[9] W. K. Hayman, Meromorphic Functions, Oxford Math. Monogr., Clarendon Press, Oxford, 1964. Search in Google Scholar

[10] P. Li and C.-C. Yang, Some further results on the unique range sets of meromorphic functions, Kodai Math. J. 18 (1995), no. 3, 437–450. 10.2996/kmj/1138043482Search in Google Scholar

[11] P. Li and C.-C. Yang, On the unique range set of meromorphic functions, Proc. Amer. Math. Soc. 124 (1996), no. 1, 177–185. 10.1090/S0002-9939-96-03045-6Search in Google Scholar

[12] E. Mues and M. Reinders, Meromorphic functions sharing one value and unique range sets, Kodai Math. J. 18 (1995), no. 3, 515–522. 10.2996/kmj/1138043489Search in Google Scholar

[13] C.-C. Yang and H.-X. Yi, Uniqueness Theory of Meromorphic Functions, Math. Appl. 557, Kluwer Academicp, Dordrecht, 2003. 10.1007/978-94-017-3626-8Search in Google Scholar

[14] L.-Z. Yang, Meromorphic functions that share two values, J. Math. Anal. Appl. 209 (1997), no. 2, 542–550. 10.1006/jmaa.1997.5329Search in Google Scholar

[15] B. Yi and Y. H. Li, Uniqueness of meromorphic functions that share two sets with CM, Acta Math. Sinica (Chin. Ser.) 55 (2012), no. 2, 363–368. Search in Google Scholar

[16] H. X. Yi, Uniqueness of meromorphic functions and question of Gross, Sci. China Ser. A 37 (1994), no. 7, 802–813. Search in Google Scholar

[17] H. X. Yi, Unicity theorems for meromorphic or entire functions. II, Bull. Aust. Math. Soc. 52 (1995), no. 2, 215–224. 10.1017/S0004972700014635Search in Google Scholar

[18] H.-X. Yi, On a question of Gross concerning uniqueness of entire functions, Bull. Aust. Math. Soc. 57 (1998), no. 2, 343–349. 10.1017/S0004972700031701Search in Google Scholar

[19] H. X. Yi, Meromorphic functions that share two sets, Acta Math. Sinica (Chin. Ser.) 45 (2002), no. 1, 75–82. 10.2996/kmj/1138043751Search in Google Scholar

Received: 2018-01-24
Accepted: 2018-11-05
Published Online: 2019-12-19
Published in Print: 2021-06-01

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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