Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Further Extending Results of Some Classes of Complex Difference and Functional Equations Jian-jun Zhang and Liang-wen Liao | Hindawi Publishing Corporation Advances in Difference Equations Volume 2010 Article ID 404582 15 pages doi 2010 404582 Research Article Further Extending Results of Some Classes of Complex Difference and Functional Equations Jian-jun Zhang and Liang-wen Liao Department of Mathematics Nanjing University Nanjing 210093 China Correspondence should be addressed to Liang-wen Liao maliao@ Received 29 March 2010 Revised 24 August 2010 Accepted 21 September 2010 Academic Editor Binggen Zhang Copyright 2010 . Zhang and . 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 ỵeI aỵ z nn 1f z CvỶ Xp jP z vn 1f z Cv m V R z f z where I Ằ U 1 h 2 . hn I h v e N u 0 V 1 2 . n and J _ 2 . m n I V e N u 0 V 1 2 . n are two finite index sets cV v 1 2 . n are distinct nonzero complex numbers a2 z Ằ e I and P z e J 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. 1. Introduction and Main Results Let f z be a meromorphic function in the complex plane. We assume that the reader is familiar with the standard notations and results in Nevanlinna s value distribution theory of meromorphic functions such as the characteristic function T r f proximity function mfr f counting function N r f the first and second main theorems see . 1-4 . We also use Nfr f to denote the counting function of the poles of f z whose every pole is counted only once. The notation Sfr f denotes any quantity that satisfies the condition S r f o Tfrf as r TO possibly outside an exceptional set of r of finite linear measure. A meromorphic function afz is .
