Abstract

In this paper, we prove that two meromorphic functions f and g must be linked by a quasi-Möbius transformation if they share a pair of small functions ignoring multiplicities and share other four pairs of small functions with multiplicities truncated by 2. We also show that two meromorphic functions which share q (q ≥ 6) pairs of small functions ignoring multiplicities are linked by a quasi-Möbius transformation. Moreover, in our results, the zeros with multiplicities more than a certain number are not needed to be counted in the condition sharing pairs of small functions of meromorphic functions. These results are generalization and improvements of some recent results.