Results 211 to 220 of about 6,522 (226)

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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Hyers–Ulam Stability of Euler’s Differential Equation

Results in Mathematics, 2015
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Popa, Dorian, Pugna, Georgiana
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Hyers–Ulam stability of hypergeometric differential equations

Aequationes mathematicae, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abdollahpour, Mohammad Reza, Rassias, Michael Th.   +1 more
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Hyers–Ulam stability of impulsive integral equations

Bollettino dell'Unione Matematica Italiana, 2018
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Zada, Akbar, Riaz, Usman, Khan, Farhan Ullah   +2 more
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HYERS–ULAM–RASSIAS STABILITY FOR NONAUTONOMOUS DYNAMICS

Rocky Mountain Journal of Mathematics
The authors study semilinear equations \begin{align*} x'&=A(t)x+f(t,x),\\ x_{n+1}&=A_nx_n+f_n(x_n) \end{align*} on the nonnegative half-line in a Banach space \(X\). Provided the linear part is uniformly exponentially stable, Hyers-Ulam-Rassias stability is established, if the (uniform) Lipschitz constant of the nonlinearity is small.
Dragičević, Davor, Jurčević Peček, Nevena   +1 more
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Hyers-Ulam and Hyers-Ulam-Rassias stability of nonlinear integral equations with delay

2011
Abstract. 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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Hyers-Ulam stability of \(k\)-Fibonacci functional equation

2011
Summary: Let denote by \(F_{k,n}\) the \(n\)th \(k\)-Fibonacci number where \(F_{k,n}=kF_{k,n-1}+F_{k,n-2}\) for \(n\geq 2\) with initial conditions \(F_{k,0} = 0\), \(F_{k,1}=1\), we may derive a functional equation \(f(k, x) = kf(k, x - 1) + f(k, x - 2)\).
Bidkham, M., Hosseini, M.
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Hyers–Ulam and Hyers–Ulam–Rassias Stability of Volterra Integral Equations with Delay

2009
Considerable 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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Subadditive Multifunctions and Hyers-Ulam Stability

1987
A multifunction F from an Abelian semigroup (S,+) into the family of all nonempty closed convex subsets of a Banach space (X, ║·║) is called subadditive provided that F(x+y) ⊂ F(x) + F(y) for all x, y ∈ S. We show that if all the values of a subadditive multifunction F are uniformly bounded then F admits an additive selection, i.e. a homomorphism a: S →
Zbigniew Gajda, Roman Ger
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