一般四次方程的稳定性(英文)  

On the Stability of the Generalized Quartic Functional Equation

作　　者：玉强[1] 郭艳平[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《四川师范大学学报（自然科学版）》2013年第5期703-707,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：supported by the National Natural Science Foundation of China(10971123)~~

摘　　要：关于泛函方程的稳定性研究源自Ulam提出的关于群同态一个问题.近几十年来关于Banach空间中的设值泛函问题取得众多成果.研究了一般的四次泛函方程f(ax+by)+f(ax-by)=a2b2f(x+y)+a2b2f(x-y)+2a2(a2-b2)f(x)-2b2(a2-b2)f(y)的通解及其在Banach空间上的Hyers-Ulam-Rassias稳定性(对任意固定的整数a≠-1,0,1,b≠0和a±b≠0).证明了上述方程等价于f(ax+y)+f(ax-y)=a2f(x+y)+a2f(x-y)+2a2(a2-1)f(x)-2(a2-1)f(y),并获得该泛函方程的Hyers-Ulam-Rassias稳定性定理.The stability problem of functional equations originated from a question of Ulam concerning the stability of group homomorphisms. Set-valued functions in Banach spaces have been developed in the past decades. In this paper, we achieve the general solution and the generalized Hyers-Ulam-Rassias stability theorem for quartic functional equation for any fixed integers a, b with a ≠ 1,0,1, b # 0 and a ＋ b #0. We prove that the functional equation is equivalent to the equation

关 键 词：Hyers—Ulam—Rassias稳定性 通解 四次映射 

分 类 号：O174[理学—数学]