A journey from UPM to SUPMWS

Articles in Press

Document Type : Research Paper

Authors
Abhijit Banerjee
Jhilik Banerjee
Department of Mathematics, University of Kalyani, West Bengal 741235, India
10.22075/ijnaa.2025.36926.5406
Abstract
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 $4 \leq n \leq 6$.
Keywords
Uniqueness polynomial
SUPM
wider sense
meromorphic functions
shared sets
[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.
International Journal of Nonlinear Analysis and Applications

Articles in Press, Corrected Proof
Available Online from 02 July 2026

  • Receive Date 17 February 2025
  • Accept Date 07 April 2025