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Result on value distribution of meromorphic functions | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 9، دوره 17، شماره 5، مرداد 2026، صفحه 109-116 اصل مقاله (324.37 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.30985.4534 | ||
| نویسندگان | ||
| Harina P Waghamore* ؛ Vijaylaxmi S B | ||
| Department of Mathematics, Jnanabharathi Campus, Bangalore University, Bengaluru-560 056, India | ||
| تاریخ دریافت: 29 خرداد 1402، تاریخ پذیرش: 28 شهریور 1403 | ||
| چکیده | ||
| 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]. | ||
| کلیدواژهها | ||
| Meromorphic function؛ Difference polynomials؛ Uniqueness | ||
| مراجع | ||
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[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. | ||
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