TWO MEROMORPHIC FUNCTIONS SHARING FOUR PAIRS OF SMALL FUNCTIONS

TWO MEROMORPHIC FUNCTIONS SHARING FOUR PAIRS OF SMALL FUNCTIONS

The purpose of this paper is twofold. The first is to show that two meromorphic functions f and g must be linked by a quasi-$M{\ddot{o}}bius$ transformation if they share a pair of small functions regardless of multiplicity and share other three pairs of small functions with multiplicities truncated to level 4. We also show a quasi-$M{\ddot{o}}bius$ transformation between two meromorphic functions if they share four pairs of small functions with multiplicities truncated by 4, where all zeros with multiplicities at least k > 865 are omitted. Moreover the explicit $M{\ddot{o}}bius$-transformation between such f and g is given. Our results are improvement of some recent results.