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Uniqueness of meromorphic (entire) functions regarding general difference-differential polynomials | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 16 اسفند 1403 اصل مقاله (364.54 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.34302.5121 | ||
| نویسندگان | ||
| Harina P. Waghamore* 1؛ Megha M. Manakame2 | ||
| 1Department of Mathematics, Jnanabharathi Campus, Bangalore University, Bangalore, 560 056, India | ||
| 2Department of Mathematics, Jnanabharathi Campus, Bangalore University, Bangalore, 560 056, India | ||
| تاریخ دریافت: 11 خرداد 1403، تاریخ پذیرش: 26 تیر 1403 | ||
| چکیده | ||
| In this article, we study the uniqueness of higher order difference-differential polynomial $\Delta_{c}^{u}f(z)$ and meromorphic(entire) functions with weights $l\geq 2$, $l=1$ and $l=0$. We obtained the results which generalize and extend due to [2, 13]. | ||
| کلیدواژه‌ها | ||
| Meromorphic functions؛ difference operator؛ weighted sharing؛ uniqueness | ||
| مراجع | ||
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[1] A. Banerjee, Meromorphic functions sharing one value, Int. J. Math. Math. Sci. 22 (2005), 3587–3598. [2] A. Banerjee and S. Majumder, Uniqueness of certain type of differential-difference and difference polynomials, Tamkang J. Math. 49 (2018), no. 1, 1–24. [3] Y.M. Chiang and S.J. Feng, On the Nevanlinna characteristic of f(z + c) and difference equations in the complex plane, Ramanujan J. 16 (2008), no. 1, 105–129. [4] G. Haldar, Uniqueness of entire functions concerning differential-difference polynomials sharing small functions, J. Anal. 30 (2022), 785–806. [5] W.K. Hayman, Meromorphic Functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964. [6] 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. [7] I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Elliptic Equ. 46 (2001), no. 3, 241–253. [8] I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J. 161 (2001), 193–206. [9] K. Liu, X. Liu, and T. Cao, Some results on zeros and uniqueness of difference-differential polynomials, Appl. Math. J. Chinese Univ. Ser. B 27 (2012), no. 1, 94–104. [10] 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. [11] 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. [12] A. Shaw, Distribution of values of difference operators concerning weakly weighted sharing, J. Appl. Math. Inf. 40 (2022), no. 3-4, 545–562. [13] H.P. Waghamore and S.H. Naveenkumar, Result on certain type of differential-difference and difference polynomials of meromorphic functions, Southeast Asian Bull. Math. 46 (2022), no. 3. [14] C.C. Yang and H.X. Yi, Uniqueness Theory of Meromorphic Functions, Science Press, Kluwer Academic Publishers Group, Dordrecht, 2003. [15] L. Yang, Value Distribution Theory, Translated and revised from the 1982 Chinese original, Springer-Verlag, Berlin, 1993. | ||
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