Author/Authors :
-، - نويسنده LMIB & School of Mathematics and Systems Science, Beihang University, Beijing, 100191, China. Zhang, Y. Y. , -، - نويسنده LMIB & School of Mathematics and Systems Science, Beihang University, Beijing, 100191, China. Gao, Z. S. , -، - نويسنده LMIB & School of Mathematics and Systems Science, Beihang University, Beijing, 100191, China. Zhang, J. L.
Abstract :
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 order transcendental meromorphic solutions for complex difference equation $prod^n_{j=1}f(z+c_j)=P(f(z))/Q(f(z))$ are also investigated.
