Stability of Functional Equations in Several Variables  

作　　者：Deng Hua ZHANG Huai Xin CAO 

机构地区：[1]College of Mathematics and Information Science,Shaanxi Normal University

出　　处：《Acta Mathematica Sinica,English Series》2007年第2期321-326,共6页数学学报（英文版）

基　　金：partly supported by the National Natural Science Foundation of China(19771056)

摘　　要：We prove a generalization of Hyers＇ theorem on the stability of approximately additive mapping and a generalization of Badora＇s theorem on an approximate ring homomorphism. We also obtain a more general stability theorem, which gives the stability theorems on Jordan and Lie homomorphisms. The proofs of the theorems given in this paper follow essentially the D. H. Hyers-Th. M. Rassias approach to the stability of functional equations connected with S. M. Ulam＇s problem.We prove a generalization of Hyers＇ theorem on the stability of approximately additive mapping and a generalization of Badora＇s theorem on an approximate ring homomorphism. We also obtain a more general stability theorem, which gives the stability theorems on Jordan and Lie homomorphisms. The proofs of the theorems given in this paper follow essentially the D. H. Hyers-Th. M. Rassias approach to the stability of functional equations connected with S. M. Ulam＇s problem.

关 键 词：STABILITY functional equation  Jordan homomorphism  Lie homomorphism 

分 类 号：O175[理学—数学]