相关论文: Stability of Derivations on Hilbert $C^*$-Modules
The purpose of this paper is to give a sufficient condition for (strong) stability of non-proper smooth functions (with respect to the Whitney $C^\infty$-topology). We show that a Morse function is stable if it is end-trivial at any point…
In this paper, we obtain the general solution and the generalized Hyers-Ulam Rassias stability of the functional equation $$f(2x+y)+f(2x-y)=4(f(x+y)+f(x-y))-{3/7}(f(2y)-2f(y))+2f(2x)-8f(x).$$
In this paper we will investigate the solutions and stability of the generalized variant of Wilson's functional equation $$ (E):\;\;\;\; f(xy)+\chi(y)f(\sigma(y)x)=2f(x)g(y),\; x,y\in G,$$ where $G$ is a group, $\sigma$ is an involutive…
In this paper, we introduce the concept of Continuous $\ast$-g-Frame in Hilbert $C^{\ast}$-Modules and we establish some results. We also discuss the stability problem for Continuous $\ast$-g-Frame.
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…
We investigate the generalized derivations and show that every generalized derivation on a simple Hilbert $C^*$-module either is closable or has a dense range. We also describe dynamical systems on a full Hilbert $C^*$-module ${\mathcal M}$…
In this paper, we establish the generalized Hyers--Ulam--Rassias stability of $C^*$-ternary ring homomorphisms associated to the Trif functional equation \begin{eqnarray*} d \cdot C_{d-2}^{l-2} f(\frac{x_1+... +x_d}{d})+…
In this paper, we consider the Cauchy-type problem for a nonlinear differential equation involving $\Psi$-Hilfer fractional derivative and prove the existence and uniqueness of solutions in the weighted space of functions. The Ulam--Hyers…
In this paper, we study the generalized Hyers-Ulam stability of Euler-Lagrange type cubic functional equation of the form \begin{align*} 2mf(x + my) + 2f(mx - y) = (m^3 + m)[f(x+ y) + f(x - y)] + 2(m^4 - 1)f(y) \end{align*} for all $x,y \in…
We prove that an interesting result concerning generalized Hyers-Ulam-Rassias stability of a linear functional equation obtained in 2014 by S.M. Jung, D. Popa and M.T. Rassias in Journal of Global Optimization is a particular case of a…
By means of the recent $\psi$-Hilfer fractional derivative and of the Banach fixed-point theorem, we investigate stabilities of Ulam-Hyers, Ulam-Hyers-Rassias and semi-Ulam-Hyers-Rassias on closed intervals $[a,b]$ and $[a,\infty)$ for a…
This paper presents finite-time and fixed-time stabilization results for inhomogeneous abstract evolution problems, extending existing theories. We prove well-posedness for strong and weak solutions, and estimate upper bounds for settling…
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…
We introduce a fairly general concept of functional equation for $k$-tuples of functions $f_1,\dots,f_k\colon X \to Y$ between arbitrary sets. The homomorphy equations for mappings between groups and other algebraic systems, as well as…
Using the fixed point method of the stability of the Jensen's functional equation, we proved the Hyers-Ulam-Rassias stability and super stability of involution on Banach algebra and find some conditions that with them a Banach algebra with…
We study the dynamics of a quantum system having Hilbert space of finite dimension $d_{\mathrm{H}}$. Instabilities are possible provided that the master equation governing the system's dynamics contain nonlinear terms. Here we consider the…
Using the direct method, we prove the generalised Hyers-Ulam stability of the following functional equation \begin{equation} \phi(x+y, z+w)+\phi(x-y, z-w)-2 \phi(x, z)-2 \phi(x, w)=0 \end{equation} in modular space satisfying the Fatou…
In this article we deal with the stability and convergence of numerical solutions of nonlinear evolution equations of the form $A(u(t))+f(u(t))=u'(t)$, the numerical analysis of solutions to this problems will be performed using some…
In this paper, we discuss the Hyers-Ulam stability of closable (unbounded) operators with several interesting examples. We also present results pertaining to the Hyers-Ulam stability of the sum and product of closable operators to have the…
We prove a stability theorem for finite-dimensional analytic inverse problems. Let \(U\subset\R^m\) be an open parameter set, let \(F(p)\) be a boundary measurement operator, and let \(R(p)\) be the finite-dimensional quantity to be…