四次方程的广义Hyers—Ulam—Rassias稳定性
2008
用不动点的择一性研究了四次方程的广义Hyers-Ulam—Rassias稳定性.证明了如果映射厂:X→Y满足f(0)=0,||(Df)(z,y)||≤φ(x,y)(任意x,y∈X)且 0≤L〈1,使得映射x│→φ(x):=φ(x/2,0)满足φ(x)≤L2^4φ(x/2)(任意x∈X),则存在惟一的四次映射V:X→Y,使得||f(x)-V(x)||≤(L/(2(1-L)))φ(x)(任意x∈X).
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