Uniqueness of meromorphic functions with deficient values and unique range sets of small cardinalities

Abstract. We give sufficient conditions for a subset \(S\) to be a unique range set for meromorphic functions, in term of relations between the degree and the derivative index of the associated polynomial, and the deficient values of functions at \(\infty\) and \(0\). As consequences, we obtained again some classes of URS for meromorphic functions with \(11\) elements. Moreover, for classes of meromorphic functions, satisfying some hypotheses on the deficient values at \(\infty\) and \(0\), we present unique range sets with \(6\), \(7\), \(8\), \(9\), \(10\) elements. Similar results for derivatives of meromorphic functions are also obtained.