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A journey from UPM to SUPMWS | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 11 تیر 1405 اصل مقاله (440.66 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2025.36926.5406 | ||
| نویسندگان | ||
| Abhijit Banerjee؛ Jhilik Banerjee* | ||
| Department of Mathematics, University of Kalyani, West Bengal 741235, India | ||
| تاریخ دریافت: 29 بهمن 1403، تاریخ پذیرش: 18 فروردین 1404 | ||
| چکیده | ||
| In this article, we systematically develop and extend the concepts and criteria associated with the uniqueness polynomial of meromorphic functions (UPM). Starting from the foundational UPM, we extend the concept to encompass the (reduced) strong uniqueness polynomial for meromorphic functions in a wider sense ((R)SUPMWS), completing this progression. This extension marks a significant advancement in this area of research. The article consolidates and organizes all related definitions of these polynomials in a concise and systematic manner. Furthermore, we classify and analyze various categories of polynomials for degree $n$, where $4 \leq n \leq 6$. | ||
| کلیدواژهها | ||
| Uniqueness polynomial؛ SUPM؛ wider sense؛ meromorphic functions؛ shared sets | ||
| مراجع | ||
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[1] A. Banerjee and S. Mallick, On the characterizations of a new class of strong uniqueness polynomials generating unique range sets, Comput. Meth. Funct. Theo. 17 (2017), 19–45. [2] A. Banerjee and I. Lahiri, A uniqueness polynomial generating a unique range set and vice versa, Comput. Method Funct. Theo. 12 (2012), no. 2, 527–539. [3] H. Fujimoto, On uniqueness of meromorphic functions sharing finite sets, Amer. J. Math. 122 (2000), no. 6, 1175–1203 [4] H. Fujimoto, On uniqueness polynomials for meromorphic functions, Nagoya Math. J. 170 (2003), 33–46. [5] W.K. Hayman, Meromorphic Functions, Clarendon Press, Oxford, 1964. [6] H. H. Khoai, H.A. Vu, and N.H. Pham, On functional equations for meromorphic functions and applications, Arch. Math. 109 (2017), no. 6, 539–549. [7] H.H. Khoai and C.C. Yang, On the functional equation P(f) = Q(g), Adv. Com. Anal. Appl. 3 (2004), 201–208. [8] P. Li and C.C. Yang, Some further results on the unique range sets of meromorphic functions, Kodai Math. 18 (1995), 437–450. [9] F. Pakovich, On polynomials sharing preimages of compact sets, and related questions, Geom. Funct. Anal. 18 (2008), no. 1, 163–183. [10] F. Pakovich, On the equation P(f) = Q(g), where P, Q are polynomials and f, g are entire functions, Amer. J. Math. 132 (2010), 1591–1607. [11] C.C. Yang and X.H. Hua, Unique polynomials of entire and meromorphic functions, Mat. Fiz. Anal. Geom. 4 (1997), no. 3, 391–398. | ||
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