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Uniqueness of meromorphic functions sharing four small functions on annuli

  • Da Wei Meng EMAIL logo , San Yang Liu und Nan Lu
Veröffentlicht/Copyright: 19. Juli 2019
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Abstract

Under a certain condition, we propose a uniqueness theorem about meromorphic functions sharing four distinct small functions on an annulus. Two counter examples are given in order to show the certain condition is necessary. Our results generalize or improve the previous theorems due to T. B. Cao et al. and N. Wu et al.


The authors thank Prof. Pei-Chu Hu for his valuable advice. This work was partially supported by the NSF of China (11271227,11561033), the Fundamental Research Funds for the Central Universities (JB180708).


  1. (Communicated by Stanisława Kanas)

References

[1] Cao, T. B.—Yi, H. X.: On the uniqueness of meromorphic functions that share four values in one angular domain, J. Math. Anal. Appl. 358 (2009), 81–97.10.1016/j.jmaa.2009.04.043Suche in Google Scholar

[2] Cao, T. B.—Yi, H. X.: Uniqueness theorems of meromorphic functions sharing setsIMon annuli, Acta Math. Sin. (Chinese Series) 54(4) (2011), 623–632, (in Chinese).Suche in Google Scholar

[3] Cao, T. B.—Yi, H. X.—Xu, H. Y.: On the multiple values and uniqueness of meromorphic functions on annuli, Comput. Math. Appl. 58 (2009), 1457–1465.10.1016/j.camwa.2009.07.042Suche in Google Scholar

[4] Fang, M. L.: Uniqueness of admissible meromorphic functions in the unit disc, Sci. China Ser. A 42(4) (1999), 367–381.10.1007/BF02874255Suche in Google Scholar

[5] Hayman, W.: Meromorphic Functions, Oxford: Clarendon Press, 1964.Suche in Google Scholar

[6] Khrystiyanyn, A. Y.—Kondratyuk, A. A.: On the Nevanlinna theory for meromorphic functions on annuli. I, Mat. Stud. 23(1) (2005), 19–30.Suche in Google Scholar

[7] Khrystiyanyn, A. Y.—Kondratyuk, A. A.: On the Nevanlinna theory for meromorphic functions on annuli. II, Mat. Stud. 24(2) (2005), 57–68.Suche in Google Scholar

[8] Kondratyuk, A. A.—Laine, I.: Meromorphic functions in multiply connected domains. In: Fourier series methods in complex analysis, (Laine, Ilpo (eds.)), Proceedings of the workshop, Mekrijärvi, Finland, July 24–29, 2005, Univ. Juensuu Dept. Ser. No. 10 (2006), 9–111. ISBN 952-458-888-9/pbkSuche in Google Scholar

[9] Korhonen, R.: Nevanlinna theory in an annulus, value distribution theory and related topics, Adv. Complex Anal. Appl. 3 (2004), 167–179.10.1007/1-4020-7951-6_7Suche in Google Scholar

[10] Li, P.: Meromorphic functions that share four small functions, J. Math. Appl. 263 (2001), 316–326.10.1006/jmaa.2001.7607Suche in Google Scholar

[11] Li, Y. H.—Qiao, J. Y.: The uniqueness of meromorphic functions concerning small functions, Sci. China Ser. A 43(6) (2000), 581–590.10.1007/978-81-322-2113-5_12Suche in Google Scholar

[12] Lin, W. C.—Mori, S.—Tohge, K.: Uniqueness theorems in an angular domain, Tohoku Math. J. 58 (2006), 509–527.10.2748/tmj/1170347687Suche in Google Scholar

[13] Liu, H. F.—Mao, Z. Q.: Meromorphic functions in the unit disc that share slowly growing functions in an angular domain, Comput. Math. Appl. 62(12) (2011), 4539–4546.10.1016/j.camwa.2011.10.033Suche in Google Scholar

[14] Lund, M.—Ye, Z.: Logarithmic derivatives in annuli, J. Math. Anal. Appl. 356 (2009), 441–452.10.1016/j.jmaa.2009.03.025Suche in Google Scholar

[15] Lund, M.—Ye, Z.: Nevanlinna theory of meromorphic functions on annuli, Sci. China. Math. 53 (2010), 547–554.10.1007/s11425-010-0037-3Suche in Google Scholar

[16] Nevanlinna, R.: Eindentig Keitssätze in der Theorie der meromorphen Funktionen, Acta. Math. 48 (1926), 367–391.10.1007/BF02565342Suche in Google Scholar

[17] Wu, N.—Ge, Q.: On uniqueness of meromorphic functions sharing five small functions on annuli, Bull. Iranian Math. Soc. 41(3) (2015), 713–722.10.1007/s10013-013-0023-5Suche in Google Scholar

[18] Xu, H. Y.—Xuan, Z. X.: The uniqueness of analytic functions on annuli sharing some values, Abstr. Appl. Anal. 2012(1) (2014), 309–323.10.1155/2012/896596Suche in Google Scholar

[19] Yao, W. H.: Meromorphic functions sharing four small functions IM, Indian J. Pure Appl. Math. 34(7) (2003), 1025–1033.Suche in Google Scholar

[20] Yi, H. X.: Uniqueness theorems for meromorphic functions cocerning small functions, Indian J. Pure Appl. Math. 32(6) (2001), 903–914.10.1090/S0002-9939-01-06245-1Suche in Google Scholar

[21] Yi, H. X.: On one problem of uniqueness of meromorphic functions concerning small functions, Proc. Amer. Math. Soc. 130(6) (2001), 1689–1697.10.1090/S0002-9939-01-06245-1Suche in Google Scholar

[22] Yi, H. X.—Yang, C. C.: Uniqueness Theory of Meromorphic Functions, Science Press, 1995, Kluwer, 2003.Suche in Google Scholar

[23] Yang, L.: Value Distribution Theory, Berlin: Springer-Verlag/Beijing: Science Press, 1993.Suche in Google Scholar

[24] Zheng, J. H.: On uniqueness of meromorphic functions with shared values in one angular domains, Complex Var. Elliptic Equ. 48 (2003), 777–785.10.1080/02781070310001599368Suche in Google Scholar

[25] Zheng, J. H.: On uniqueness of meromorphic functions with shared values in some angular domains, Canad. J. Math. 47 (2004), 152–160.10.4153/CMB-2004-016-1Suche in Google Scholar

Received: 2018-08-09
Accepted: 2018-10-13
Published Online: 2019-07-19
Published in Print: 2019-08-27

© 2019 Mathematical Institute Slovak Academy of Sciences

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