On strong uniqueness polynomials in the wider sense and associated unique range sets of the same category

A. Banerjee, J. Banerjee

In this paper, motivated by the definition of Strong Uniqueness Polynomial for Meromorphic Functions (SUPM) as introduced by Fujimoto earlier, we have strived on the utmost generalization of the same definition and thus presented a new extended version of it namely Strong Uniqueness Polynomial for Meromorphic Functions in the Wider Sense (SUPMWS). In fact, in the last section of this article, under a remark, we have exhibited that this extension is viable, thereby justifying the introduction of the new definition. Using the SUPMWS, we also delve into investigating the generation of unique range sets with finite weight. This implies that the new definition can be effectively employed to establish unique range sets with certain characteristics, which could be significant in various applications and mathematical contexts. Our results will conveniently improve and extend a series of results in the literature. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 16(4) (2023), pp. 175-189