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Báo cáo toán học: " Some results on difference polynomials sharing values"

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học được đăng trên tạp chí toán học quốc tế đề tài: Some results on difference polynomials sharing values | Liu et al. Advances in Difference Equations 2012 2012 1 http www.advancesindifferenceequations.eom content 2012 1 1 o Advances in Difference Equations a SpringerOpen Journal RESEARCH Open Access Some results on difference polynomials sharing values Yong Liu1 2 XiaoGuang Qi 1 3 and Hongxun Yi1 Correspondence xiaoguangqi@yahoo.cn 3Department of Mathematics Jinan University Jinan 250022 Shandong P. R. China Full list of author information is available at the end of the article Springer Abstract This article is devoted to studying uniqueness of difference polynomials sharing values. The results improve those given by Liu and Yang and Heittokangas et al. 1 Introduction and main results In this article we shall assume that the reader is familiar with the fundamental results and the standard notations of the Nevanlinna theory e.g. see 1-3 . In addition we will use the notations l f to denote the exponent of convergence of zero sequences of meromorphic function f z s f to denote the order off z . We say that meromorphic functions f and g share a finite value a CM when f - a and g - a have the same zeros with the same multiplicities. For a non-zero constant c the forward difference A f z w z c - w z - z w z c - w z n 1 2 . In general we use the notation C to denote the field of complex numbers. Currently there has been an increasing interest in studying difference equations in the complex plane. Halburd and Korhonen 4 5 established a version of Nevanlinna theory based on difference operators. Ishizaki and Yanagihara 6 developed a version of Wiman-Valiron theory for difference equations of entire functions of small growth. Recently Liu and Yang 7 establish a counterpart result to the Bruck conjecture 8 valid for transcendental entire function for which s f 1. The result is stated as follows. Theorem A. Let fbe a transcendental entire function such that ơ f 1. Iff and Aff share a finite value a CM n is a positive integer and c is a fixed constant then nf - a f_ T f a for some