Related papers: Hyers-Ulam Stability of Unbounded Closable Operato…
This paper introduces the concept of Hyers-Ulam stability for linear relations in normed linear spaces and presents several intriguing results that characterize the Hyers-Ulam stability of closed linear relations in Hilbert spaces.…
In this paper, we establish a link between the Hyers-Ulam stability and the Moore--Penrose inverse, that is, a closed operator has the Hyers-Ulam stability if and only if it has a bounded Moore-Penrose inverse. Meanwhile, the stability…
Recently, Popa and Rasa [18,19] have shown the (in)stability of some classical operators defined on [0,1] and found best constant when the positive linear operators are stable in the sense of Hyers-Ulam. In this paper we show Hyers-Ulam…
The main purpose of this paper is to obtain necessary and sufficient conditions under which a nonautonomous, finite-dimensional and two-sided dynamics generated by a sequence of matrices or a linear ODE exhibits Hyers-Ulam stability.…
We explore the Hyers-Ulam stability of perturbations for a homogeneous linear differential system with $2\times 2$ constant coefficient matrix. New necessary and sufficient conditions for the linear system to be Hyers-Ulam stable are…
We establish the Hyers-Ulam stability of certain linear first-order differential equations with singularities. We then extend these results to higher-order singular linear differential equations that can be written with these first-order…
The stability problem in Ulam's sense has recently been explored in locally convex cone environments, as shown in \cite{ MNF, NR1, NR2}. In continuation of this research direction, our work examines the stability properties of the quadratic…
This paper explores the Hyers-Ulam stability of generalized Jensen additive and quadratic functional equations in \(\beta\)-homogeneous \(F\)-space, showing that approximately satisfying mappings have a unique exact approximating…
We provide several perturbation theorems regarding closable operators on a real or complex Hilbert space. In particular we extend some classical results due to Hess--Kato, Kato--Rellich and W\"ust. Our approach involves ranges of matrix…
We establish the stability of higher-order linear non-homogeneous Cauchy-Euler dynamic equations on time scales in the sense of Hyers and Ulam. That is, if an approximate solution of a higher-order Cauchy-Euler equation exists, then there…
We establish the stability of second-order linear dynamic equations on time scales in the sense of Hyers and Ulam. To wit, if an approximate solution of the second-order linear equation exists, then there exists an exact solution to the…
We analyse different kinds of stabilities for the Bessel equation and for the modified Bessel equation with initial conditions. Sufficient conditions are obtained in order to guarantee Hyers-Ulam-Rassias, $\sigma$-semi-Hyers-Ulam and…
In this work, we prove an existence theorem of the Hyers-Ulam stability for the nonlinear Volterra integral equations which improves and generalizes Castro-Ramos theorem by using some weak conditions.
In this paper, we examine the Hyers-Ulam and Hyers-Ulam-Rassias stability of solutions of a general class of nonlinear Volterra integral equations. By using a fixed point alternative and improving a technique commonly used in similar…
Hyers-Ulam of the sequence $ \{z_n\}_{n \in \mathbb{N}} $ satisfying the difference equation $ z_{i+1} = g(z_i) $ where $ g(z) = \frac{az + b}{cz + d} $ with complex numbers $ a $, $ b $, $ c $ and $ d $ is defined. Let $ g $ be loxodromic…
In \cite{bbb} the authors obtained the Hyers-Ulam stability of the functional equation $$ \int_{K}\int_{G} f(xtk\cdot y)d\mu(t)dk=f(x)g(y), \; x, y \in G ,$$ where $G$ is a Hausdorff locally compact topological group, $K$ is a copmact…
We establish the Hyers-Ulam stability of a second-order linear Hill-type $h$-difference equation with a periodic coefficient. Using results from first-order $h$-difference equations with periodic coefficient of arbitrary order, both…
We clarify the Hyers--Ulam stability (HUS) of certain first-order linear constant coefficient dynamic equations on time scales, in the case of a specific time scale with two alternating step sizes, where the exponential function changes…
In this paper, we study the Hyers-Ulam stability of the following equation \begin{multline*} \phi(x+y-z)+\phi(x+z-y)+\phi(y+z-x)=\phi (x-y)+\phi(x-z)+\phi(z-y) +\phi(x)+\phi(y) +\phi(z) \end{multline*} in modular space, with or without…
We consider Hyers-Ulam stability of a functional equation for continuous functions on a space on which a topological group acts, analogous to the additive functional equation on a group. We show, among other things, that our generalized…