On meromorphic solutions of some Fermat-type functional equations (Q6637607)

Based on the difference Nevanlinna theory, the authors study the non-existence of meromorphic solutions with hyper-order less than 1 to functional equations \(f(z)^{2}+f(z+c)^{3}=e^{P}\), \(f(z)^{2}+f(z+c)^{4}=e^{P}\), and \(f(z)^{3}+[c_{1}f(z+c)+c_{0}f(z)]^{3}=e^{P}\), where \(P\) is a polynomial. These results improve the results of \textit{F. Lü} and \textit{H. Guo} [Mediterr. J. Math. 19, No. 3, Paper No. 118, 13 p. (2022; Zbl 1492.30070)] and \textit{M. B. Ahamed} [J. Contemp. Math. Anal., Armen. Acad. Sci. 56, No. 5, 255--269 (2021; Zbl 1482.30084)].