Ulam–Hyers stabilities of a differential equation and a weakly singular Volterra integral equation
Articles > Article · 2021
Authors: Özgür EGE, Souad Ayadi, Choonkil Park
Journal of Inequalities and Applications, Journal Indexed in SCI Expanded, International, WoS, 2021, vol 2021, pp 1-12
DOI: 10.1186/s13660-020-02529-z
Summary
Abstract 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 $C([a,b])$ C ( [ a , b ] ) .