Result on value distribution of meromorphic functions

Document Type : Research Paper

Authors

Department of Mathematics, Jnanabharathi Campus, Bangalore University, Bengaluru-560 056, India

Abstract

In this article, we deal with value distribution of transcendental meromorphic functions with finite order and obtain some results which improve previous theorems given by Y. Liu, J.P. Wang, and F.H.Liu [14].

Keywords

[1] A. Banerjee, Weighted sharing of a small function by a meromorphic function and its derivative, Comput. Math. Appl. 53 (2007), no. 11, 1750–1761.
[2] Z.X. Chen and H.X. Yi, On sharing values of meromorphic functions and their differences, Results Math. 63 (2013), no. 1-2, 557–565.
[3] Y.M. Chiang and S.J. Feng, On the Nevanlinna characteristic of f(z + η) and difference equations in the complex plane, Ramanujan J. 16 (2008), no. 1, 105–129.
[4] C.Y. Fang and M.L. Fang, Uniqueness of meromorphic functions and differential polynomials, Comput. Math. Appl. 44 (2002), no. 5-6, 607–617.
[5] A.A. Goldberg and I.V. Ostrovskiı, Raspredelenie Znacheniı Meromorfnykh Funktsiı, Nauka, Moscow, 1970. [In Russian]
[6] R.G. Halburd and R.J. Korhonen, Difference analogue of the lemma on the logarithmic derivative with applications to difference equations, J. Math. Anal. Appl. 314 (2006), no. 2, 477–487.
[7] R.G. Halburd and R.J. Korhonen, Nevanlinna theory for the difference operator, Ann. Acad. Sci. Fenn. Math. 31 (2006), no. 2, 463–478.
[8] R.G. Halburd and R.J. Korhonen, Finite-order meromorphic solutions and the discrete Painlev´e equations, Proc. Lond. Math. Soc. 94 (2007), no. 2, 443–474.
[9] W.K. Hayman, Meromorphic Functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964.
[10] J. Heittokangas, R. Korhonen, I. Laine, J. Rieppo, and J. Zhang, Value sharing results for shifts of meromorphic functions, and sufficient conditions for periodicity, J. Math. Anal. Appl. 355 (2009), no. 1, 352–363.
[11] K. Ishizaki and N. Yanagihara, Wiman-Valiron method for difference equations, Nagoya Math. J. 175 (2004), 75–102.
[12] I. Laine, Nevanlinna Theory and Complex Differential Equations, De Gruyter Studies in Mathematics, 15. Walter de Gruyter & Co., Berlin, 1993.
[13] K. Liu, T. Cao, and X. Liu, Some difference results on Hayman conjecture and uniqueness, Bull. Iran. Math. Soc. 38 (2012), no. 4, 1007–1020.
[14] Y. Liu, J.P. Wang, and F.H. Liu, Some results on value distribution of the difference operator, Bull. Iran. Math. Soc. 41 (2015), no. 3, 603–611.
[15] X.G. Qi, L.Z. Yang, and K. Liu, Uniqueness and periodicity of meromorphic functions concerning the difference operator, Comput. Math. Appl. 60 (2010), no. 6, 1739–1746.
[16] C.C. Yang and H.X. Yi, Uniqueness Theory of Meromorphic Functions, Mathematics and its Applications, Kluwer Academic Publishers Group, Dordrecht, 2003.
[17] H.X. Yi and C.C. Yang, Uniqueness Theory of Meromorphic Functions, Science Press, Beijing, 1995.
[18] J. Zhang and R. Korhonen, On the Nevanlinna characteristic of f(qz) and its applications, J. Math. Anal. Appl. 369 (2010), no. 2, 537–544.

Articles in Press, Corrected Proof
Available Online from 03 May 2025
  • Receive Date: 19 June 2023
  • Accept Date: 18 September 2024