Ulam stability - Open Access .click

Mediterranean Journal of Mathematics, 2021
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Delia-Maria Kerekes, Dorian Popa
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The Hyers–Ulam stability of nonlinear recurrences

Journal of Mathematical Analysis and Applications, 2007
In the paper of \textit{D. Popa} [J. Math. Anal. Appl. 309, No. 2, 591--597 (2005; Zbl 1079.39027)] the Hyers-Ulam stability problem was proved for linear recurrences in a Banach space. In the paper under review, the authors investigate this problem for nonlinear recurrences in a metric space \((X, d)\). More precisely, they show that if \(\{x_n\}\), \(
Dorian Popa, Janusz Brzdęk
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Generalized Dichotomies and Hyers–Ulam Stability

Results in Mathematics, 2023
Consider \[ x^\prime=A(t)x+f(t,x),\,t\geq 0,\tag{1} \] where \(A:\mathbb{R}_+\to \mathbb{R}^{n\times n}\) and \(f:\mathbb{R}_+\times \mathbb{R}^n\to \mathbb{R}^n\) are continuous mappings. It is known that if the corresponding linear differential equation \(x^\prime=A(t)x\) has a uniform exponential dichotomy and \(f(t,x)\) is Lipschitz in \(x ...
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mathematics
ulam-hyers stability
ulam–hyers stability

implicit fractional differential equations
ulam-hyers-rassias stability
uniqueness

existence
hyers-ulam stability
fixed point theorem