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Generalized Dichotomies and Hyers–Ulam Stability
Results in Mathematics, 2023Consider \[ x^\prime=A(t)x+f(t,x),\,t\geq 0,\tag{1} \] 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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The Hyers–Ulam–Rassias stability of the pexiderized equations
Nonlinear Analysis: Theory, Methods & Applications, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Park, Dal-Won, Lee, Yang-Hi
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On the Hyers–Ulam Stability of Bernoulli’s Differential Equation
Russian MathematicsThe aim of this paper is to present the results on the Hyers–Ulam–Rassias stability and the Hyers–Ulam stability for Bernoulli's differential equation. The argument makes use of a fixed point approach. Some examples are given to illustrate the main results.
Shah, R., Irshad, N.
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Hyers-Ulam and Hyers-Ulam-Rassias stability of nonlinear integral equations with delay
2011Abstract. In this paper we are going to study the Hyers–Ulam–Rassias typesof stability for nonlinear, nonhomogeneous Volterra integral equations with delayon finite intervals. 1. IntroductionVolterra integral equations have been extensively studied since its appearance in1896.
Morales, J. R., Rojas, E. M.
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On Hyers-Ulam Stability of Monomial Functional Equations
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 1998The paper concerns the stability, in the sense of Hyers--Ulam, of the monomial functional equation \[ \Delta^n_y f(x)-n!f(y)=0, \] where \(x,y \in \mathbb{R}\), and \(f\) takes values in a Banach space \(B\). The stability of this equation has been already studied by \textit{L. Székelyhidi}, [C. R. Math. Acad. Sci., Soc. R. Can.
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Hyers–Ulam stability of hypergeometric differential equations
Aequationes mathematicae, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abdollahpour, Mohammad Reza +1 more
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Hyers–Ulam and Hyers–Ulam–Rassias Stability of Volterra Integral Equations with Delay
2009Considerable attention has been given to the study of the Hyers–Ulam and Hyers–Ulam–Rassias stability of functional equations (see, e.g., [HIR98, Ju01]). The concept of stability for a functional equation arises when we replace the functional equation by an inequality which acts as a perturbation of the equation.
L. P. Castro, A. Ramos
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Hyers–Ulam Stability of Euler’s Differential Equation
Results in Mathematics, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Popa, Dorian, Pugna, Georgiana
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A Gompertz Model With Conditional Hyers‐Ulam Stability
Mathematical Methods in the Applied SciencesABSTRACTWe consider the Hyers‐Ulam stability of a first‐order nonlinear differential equation based on the Gompertz model. The stability is conditionally established, based on the maximum size of the perturbation being sufficiently small and the initial condition being sufficiently large.
Douglas Anderson +2 more
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On Hyers— Ulam Stability of Hosszú’s Functional Equation
Results in Mathematics, 1994Let \(Hf(x, y):= f(x+ y- xy)+ f(xy)- f(x)- f(y)\). The following result on Hyers-Ulam stability of the Hosszú equation \(Hf(x, y)= 0\) is proved: Let \(f: \mathbb{R}\to \mathbb{R}\) be a function satisfying \(|Hf(x, y)|\leq \delta\) for some \(\delta> 0\). There exists an additive function \(a: \mathbb{R}\to \mathbb{R}\) such that the difference \(f- a\
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