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Journal of Complex Analysis
Volume 2015, Article ID 960204, 8 pages
http://dx.doi.org/10.1155/2015/960204
Research Article

Good Linear Operators and Meromorphic Solutions of Functional Equations

1School of Mathematics, Shandong University, Jinan, Shandong 250100, China
2Department of Physics and Mathematics, Joensuu Campus, University of Eastern Finland, P.O. Box 111, 80101 Joensuu, Finland

Received 23 March 2015; Accepted 24 April 2015

Academic Editor: Bao Qin Li

Copyright © 2015 Nan Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Nevanlinna theory provides us with many tools applicable to the study of value distribution of meromorphic solutions of differential equations. Analogues of some of these tools have been recently developed for difference, -difference, and ultradiscrete equations. In many cases, the methodologies used in the study of meromorphic solutions of differential, difference, and -difference equations are largely similar. The purpose of this paper is to collect some of these tools in a common toolbox for the study of general classes of functional equations by introducing notion of a good linear operator, which satisfies certain regularity conditions in terms of value distribution theory. As an example case, we apply our methods to study the growth of meromorphic solutions of the functional equation , where is a linear polynomial in and , where is good linear operator, is a polynomial in with degree deg , both with small meromorphic coefficients, and is a meromorphic function.