Advances in Difference Equations
Volume 2010 (2010), Article ID 404582, 15 pages
Research Article

Further Extending Results of Some Classes of Complex Difference and Functional Equations

Department of Mathematics, Nanjing University, Nanjing 210093, China

Received 29 March 2010; Revised 24 August 2010; Accepted 21 September 2010

Academic Editor: Binggen Zhang

Copyright © 2010 Jian-jun Zhang and Liang-wen Liao. 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.


The main purpose of this paper is to present some properties of the meromorphic solutions of complex difference equation of the form λIαλ(z)(ν=1nf(z+cν)lλ,ν)/μJβμ(z)(ν=1nf(z+cν)mμ,ν)=R(z,f(z)), where I={λ=(lλ,1,lλ,2,,lλ,n)lλ,ν  ∪  {0}, ν=1,2,,n} and J={μ=(mμ,1,mμ,2,,mμ,n)mμ, ν  ∪  {0}, ν=1,2,,n} are two finite index sets, cν(ν=1,2,,n) are distinct, nonzero complex numbers, αλ(z)(λI) and βμ(z)(μJ) are small functions relative to f(z),R(z,f(z)) is a rational function in f(z) with coefficients which are small functions of f(z). We also consider related complex functional equations in the paper.