Results 111 to 120 of about 1,382 (134)

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
openaire   +3 more sources

On Hyers— Ulam Stability of Hosszú’s Functional Equation

Results in Mathematics, 1994
Let \(Hf(x, y):= f(x+ y- xy)+ f(xy)- f(x)- f(y)\). 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\
openaire   +1 more source

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
openaire   +1 more source

On Hyers--Ulam stability of Wilson's functional equation

Aequationes Mathematicae, 2000
The paper investigates the stability problem for spherical functions in the Hyers-Ulam sense. Let \((G,+)\) be a topological abelian group and let \(K\) be a compact subgroup of automorphisms of G with the normalized Haar measure \(\mu\). Further, let the map \[ k\mapsto ky\in G,\qquad k\in K , \] where \(ky\) stands for the action of \(k\in K\) on \(y\
openaire   +2 more sources

On Hyers-Ulam Stability of Monomial Functional Equations

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 1998
The 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.
openaire   +2 more sources

Hyers—Ulam stability of isometries on Banach spaces

Aequationes Mathematicae, 1999
The paper is a brief survey on the stability of isometries on real Banach spaces. An \(\varepsilon\)-isometry between two Banach spaces \(X,Y\) is a map \( f:X\to Y \) satisfying \( |\|f(x)-f(y)\|- \|x-y\||\leq \varepsilon, \forall x,y\in X.\) For an isometry \(U:X\to Y \) let dist\((f,U)=\inf\{\|f(x)-U(x)\|:x\in X\}.\) The paper is concerned with the ...
openaire   +1 more source

Ulam–Hyers–Rassias stability of neutral stochastic functional differential equations

Stochastics, 2022
Mohamed Rhaimá, Lassaad McHiri, Tomáš Caraballo   +2 more
exaly  

Ulam–Hyers stability of a nonlinear fractional Volterra integro-differential equation

Applied Mathematics Letters, 2018
José Vanterler Costa Sousa, E Capelas de Oliveira   +1 more
exaly  

A Generalization of the Hyers–Ulam–Rassias Stability of Jensen's Equation

Journal of Mathematical Analysis and Applications, 1999
Yang-Hi Lee, Kil-Woung Jun
exaly  

The generalized Hyers–Ulam–Rassias stability of a cubic functional equation

Journal of Mathematical Analysis and Applications, 2002
Hark-Mahn Kim, Kil-Woung Jun
exaly