Copyright © 2010 Jian-jun Zhang and Liang-wen Liao. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The main purpose of this paper is to present some properties of the meromorphic solutions of complex difference equation of the form , where and are two finite index sets, are distinct, nonzero complex numbers, and are small functions relative to is a rational function in with coefficients which are small functions of . We also consider related complex functional equations in the paper.