‎In this paper‎, ‎we give some necessary conditions for a complex‎ ‎difference equation of Malmquist type‎ $$‎sum^n_{j=1}f(z+c_j)=frac{P(f(z))}{Q(f(z))}‎,$$ ‎where $n(in{mathbb{N}})geq{2}$‎, ‎and $P(f(z))$ and $Q(f(z))$ are‎ ‎relatively prime polynomials in $f(z)$ with small functions as‎ ‎coefficients‎, ‎admitting a meromorphic function of finite order‎. ‎Moreover‎, ‎the properties of finite o...