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一般四次方程的稳定性(英)

, PP. 703-707

Keywords: Hyers-Ulam-Rassias稳定性,通解,四次映射

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Abstract:

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

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