模糊几乎二次函数
Fuzzy almost quadratic functions
摘要：
用模糊意义下的二次函数逼近模糊概二次函数。更准确地说，我们建立了二次函数方程$f(x+y)+f(x-y)=2f(x)+2f(y)$的模糊Hyers-Ulam-Rassias稳定性.我们的结果可以看作是在赋范空间框架下稳定性现象的推广。我们还证明了一个广义版本的Pexiderized二次函数方程$f(x+y)+f(x-y)=2g(x)+2h(y)$的模糊稳定性。
英文摘要：
We approximate a fuzzy almost quadratic function by a quadratic function in a fuzzy sense. More precisely, we establish a fuzzy Hyers--Ulam--Rassias stability of the quadratic functional equation $f(x+y)+f(x-y)=2f(x)+2f(y)$. Our result can be regarded as a generalization of the stability phenomenon in the framework of normed spaces. We also prove a generalized version of fuzzy stability of the Pexiderized quadratic functional equation $f(x+y)+f(x-y)=2g(x)+2h(y)$.
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