In this work we study the Ulam–Hyers stability of a differential equation. Its proof is based on the Banach fixed point theorem in some space of continuous functions equipped with the norm $\|\cdot \|_{\infty }$ . Moreover, we get some results on the Ulam–Hyers stability of a weakly singular Volterra integral equation using the Banach contraction principle in the space of continuous functions $C([a,b])$ .

中文翻译：

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微分方程和弱奇异Volterra积分方程的Ulam-Hyers稳定性

在这项工作中，我们研究了一个微分方程的Ulam-Hyers稳定性。它的证明是基于某些连续函数的Banach不动点定理，该函数配备了标准$ \ | \ cdot \ | _ {\ infty} $。此外，在连续函数$ C（[a，b]）$的空间中，我们使用Banach压缩原理对弱奇异Volterra积分方程的Ulam-Hyers稳定性给出了一些结果。