Growth of meromorphic solutions for complex difference‎ ‎equations of Malmquist type

In this paper‎, ‎we give some necessary conditions for a complex‎ ‎difference equation of Malmquist type‎ ‎∑j=1nf(z+cj)=P(f(z))Q(f(z))‎, ‎where n(∈N)≥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 order transcendental meromorphic‎ ‎solutions for complex difference equation‎ ‎∏nj=1f(z+cj)=P(f(z))/Q(f(z)) are also investigated.