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Further results about the transcendental meromorphic solution of a special Fermat-type equation | ||
International Journal of Nonlinear Analysis and Applications | ||
مقاله 2، دوره 15، شماره 1، فروردین 2024، صفحه 3-7 اصل مقاله (324.92 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.29809.4266 | ||
نویسندگان | ||
Chaithra C. N.* ؛ S. H. Naveenkumar؛ H. R. Jayarama | ||
Department of Mathematics, Presidency University, Bengaluru-560 064, India | ||
تاریخ دریافت: 14 بهمن 1401، تاریخ پذیرش: 07 خرداد 1402 | ||
چکیده | ||
In this paper, we mainly investigate the finite order transcendental meromorphic solutions of Fermat-type equations and also we consider here the linear difference operator of meromorphic function. In addition, we extend some recent results obtained in [1]. The example is exhibited to validate certain claims of the main result. | ||
کلیدواژهها | ||
Fermat-type equation؛ Shift equation؛ Nevanlinna theory؛ Finite order؛ Entire and Meromorphic solutions | ||
مراجع | ||
[1] A. Banerjee and T. Biswas, On the transcendental solutions of Fermat type delay-differential and c-shift equations with some analogous results, arXiv preprint arXiv:2103.08363, 2021. [2] C.N. Chaithra, S.H. Naveenkumar and H.R. Jayarama, On the transcendental solution of the Fermat type q-shift equation, Electronic J. Math. Anal. Appl. 11 (2023), no. 2, 1–7. [3] C.N. Chaithra, S.H. Naveenkumar and H.R. Jayarama, Uniqueness of meromorphic function sharing two values concerning differential-difference polynomial and it’s kth derivative, Math. Engin. Sci. Aerospace 14 (2023), no. 1, 129–144. [4] 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. [5] R.G. Halburd and R.J. Korhonen, Nevanlinna theory for the difference operator, arXiv preprint math/0506011, 2005. [6] W.K. Hayman, Meromorphic Functions, Oxford Clarendon Press, 1964. [7] 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. [8] H.R. Jayarama, S.H. Naveenkumar and C.N. Chaithra, Uniqueness of L-functions relating to possible Differential polynomial share with some finite weight, Ganita 72 (2022), no. 2, 93–101. [9] I. Laine, Nevanlinna Theory and Complex Differential Equations, De Gruyter, 1993. [10] X. Qi, Y. Liu and L. Yang, On meromorphic solutions of certain type of difference equations, Bull. Iran. Math. Soc. 14 (2015), no. 1, 281–289. [11] X. Qi, Value distribution and uniqueness of difference polynomials and entire solutions of difference equations, Ann. Polanici Math. 2 (2011) 129–142. [12] H.P. Waghamore and S.H. Naveenkumar, Results on certain type of q-shift difference polynomials, J. Anal. 28 (2020), no. 3, 733–740. | ||
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