Meromorphic solutions of discrete functional equations

借助于值分布理论，我们考虑了复域上的函数方程。特别讨论了离散函数方程，如差分方程组和施罗德方程。要做到这一点，我们关注的是增长的构成，整个功能增长缓慢。我们得到了没有例外集的复合函数的一个估计。作为应用，我们将这个估计应用于具有超越函数的Schroeder方程。我们还从复动力学的角度考虑了函数方程f(G(Z))=R(f(Z))。通过一些已知结果的例子的可视化，我们提出了一个问题。我们一般都能解决这个问题。

We consider functional equations in the complex domains by means of the value distribution theory. In particular, discrete functional equations are discussed, for examples, difference equations and Schroeder equations. To do this, we are concerned with the growth of the composition of entire functions of slow growth. We obtain an estimate for composite functions without exceptional set. As an application, we apply this estimate to a Schroeder equation with a transcendental function. We also consider a functional equation f(G(z))=R(f(z)) from the view points of complex dynamics. By visualizations of some examples for known result, we posed a question. We solve it in general.