On Uniqueness of Meromorphic Functions Ignoring Multiplicity Concerning a Question of Yi

Let S = {z ∈ C : P(z) = zn+azn−1+b = 0}, where a, b ∈ C be nonzero constants satisfying b an ̸= (−1)n(n − 1)n−1 nn . The uniqueness of meromorphic functions sharing S counting multiplicity(resp. with weight 2) has been studied by Yi ([18]) (resp. Lahiri, Banerjee ([12])). In this paper, we consider the uniqueness of meromorphic functions sharing S ignoring multiplicity. We first obtain the analog of Yi’s Theorem 2 ([18]). Next, we show that S is a unique range set for the class of meromorphic functions ignoring multiplicity of higher multiplicities of either zeros or poles, which different from S. Mallick - D. Sarkar’s ([13]). We discuss some applications of the main result. Our results are inspired by a work of Yi ([18]) and Khoai ([11]).