On uniqueness of meromorphic functions partially sharing values with their \(q\)-shifts (Q2048978)

The authors consider the uniqueness of meromorphic functions of order zero. They prove some results concerning the truncated sharing of four values by a meromorphic function \(f(z)\) with its \(q\)-shift \(f(qz)\). In one of their results the authors use a modified notion of truncated sharing of values by introducing a concept of level that further regulates the multiplicities of \(a\)-points. The results of the paper, in some sense, extend some known results on the uniqueness of meromorphic functions and their shifts.