By means of the Nevanlinna theory, the author treats functional equations of the form
where , , are polynomials of degree with . The author studies growth properties and the pole distribution of meromorphic solutions of (1).
In case , , the functional equation is known as a -difference equation. Recent developments in the study of nonlinear -difference equations in the complex plane can be found in, e.g., [J. Zhang and R. Korhonen, J. Math. Anal. Appl. 369, No. 2, 537–544 (2010; Zbl 1198.30033)] and [X.-M. Zheng and Z.-X. Chen, ibid. 361, No. 2, 472–480 (2010; Zbl 1185.39006)]. The author obtaines generalizations of the results in the cited papers.