Hyers–Ulam stability with respect to gauges
Hyers–Ulam stability with respect to gauges
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DOI：
10.1016/j.jmaa.2017.04.022
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发表时间：
2017-09
影响因子：
1.3
通讯作者：
J. Brzdȩk;D. Popa;I. Raşa
中科院分区：
文献类型：
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作者：
J. Brzdȩk;D. Popa;I. Raşa
我们建议对耶尔-乌拉姆稳定问题采取一种新的办法。即，设A， B是（实或复）线性空间，L: A→B是一个线性算子，N:= k er L， ρ A和ρ B分别是A和B上的半量规。如果对于每一个x∈A，使得ρ B (L x)≤1，存在z∈N且ρ A (z−x)≤K，则我们说L是h稳定且常数K≥0。利用这个定义，我们得到了一些微分方程近似解的相当一般的结果。
We suggest a somewhat new approach to the issue of Hyers–Ulam stability. Namely, let A, B be (real or complex) linear spaces, L: A→ B be a linear operator, N:= k e r L, and ρ A and ρ B be semigauges on A and B, respectively. We say that L is HU-stable with constant K≥ 0 if for each x∈ A such that ρ B (L x)≤ 1 there exists z∈ N with ρ A (z− x)≤ K. With that definition we obtain quite general outcomes concerning approximate solutions to some differential equations.