Journal of the
Korean Mathematical Society JKMS

In this paper, we exhibit the equivalence between different notions of unique range sets, namely, unique range sets, weighted unique range sets and weak-weighted unique range sets under certain conditions. Also, we present some uniqueness theorems which show how two meromorphic functions are uniquely determined by their two finite shared sets. Moreover, in the last section, we make some observations that help us to construct other new classes of unique range sets.

Keywords: Unique range set, weighted set sharing, value distribution theory

MSC numbers: Primary 30D30, 30D20, 30D35

Supported by: The research work of the first and the second authors are supported by the Department of Higher Education, Science and Technology \text{\&} Biotechnology, Govt.~of West Bengal under the sanction order no.~216(sanc) /ST/P/S\text{\&}T/16G-14/2018 dated 19/02/2019. The third and fourth authors are thankful to the Council of Scientific and Industrial Research, HRDG, India for granting Junior Research Fellowship (File No.: 09/106(0179)/2018-EMR-I \text{\&} 08/525(0003)/2019-EMR-I respectively) during the tenure of which this work was done