Abstract In this article, by utilizing the properties of elliptic functions, we characterize the meromorphic solutions of Fermat-type functional equations f (z) ^n+f (L (z) ) ^m=1 over the complex plane C, where L (z) is a nonconstant entire function, and m and n are two positive integers. As applications, we also investigate the meromorphic solutions of Fermat-type difference and q -difference equations.
Feng Lü (Thu,) studied this question.