Related papers: Stability of additive-quadratic functional equatio…
In this paper we obtain a result on Hyers-Ulam stability of the linear functional equation in a single variable $f(\varphi(x)) = g(x) \cdot f(x)$ on a complete metric group.
In this article, by using the fixed point method, we prove the generalized Hyers--Ulam stability of biderivations from an algebra to a modular space, associated to bi-additive s-functional inequalities.
We show that noncommutative analog of additive functional equation has Hyers-Ulam stability on amenable discrete quantum (semi)groups. This generalizes an old classical result.
In this paper, by using the orthogonally fixed point method, we prove the Hyers-Ulam stability and the hyperstability of orthogonally 3-Lie homomorphisms for additive $\rho$-functional equation in 3-Lie algebras.\\ Indeed, we investigate…
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…
In this paper, we investigate the generalized Hyers--Ulam--Rassias stability of the system of functional equations $$f(xy)=f(x)f(y), \qquad\qquad. f(2x+y)+f(2x-y)=2f(x+y)+2f(x-y)+12f(x), $$ on Banach algebras. Indeed we establish the…
We approximate a fuzzy almost quadratic function by a quadratic function in a fuzzy sense. More precisely, we establish a fuzzy Hyers--Ulam--Rassias stability of the quadratic functional equation $f(x+y)+f(x-y)=2f(x)+2f(y)$. Our result can…
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.
Addressing stability in functional equations is a critical task with broad implications across mathematics and its applications. In this paper, we present a novel direct method for proving the stability of the following equation,…
In this paper, we obtain the general solution and investigate the generalized Hyers-Ulam-Rassias stability for the new mixed type additive and cubic functional equation $$3f(x+3y) - f(3x + y)=12[f(x+y)+f(x-y)]-16[f(x)+f(y)] + 12f(2y) -…
The Hyers--Ulam stability of the conditional quadratic functional equation of Pexider type f(x+y)+f(x-y)=2g(x)+2h(y), x\perp y is established where \perp is a symmetric orthogonality in the sense of Ratz and f is odd.
The stability problem in Ulam's sense has recently been explored in locally convex cone environments, as shown in \cite{ MNF, NR1, NR2}. In continuation of this research direction, our work examines the stability properties of the quadratic…
Hyre-Ulam stability of functional equation in single variable is studied in non-triangular metric spaces. We derive it as applications of some fixed point results developed on the said structure. A general version of Baker's theorem is also…
In this paper, we give a proof of the Hyers-Ulam stability of the Jensen functional equation $$f(xy)+f(x\sigma(y))=2f(x),\phantom{+} x,y\in{G},$$ where $G$ is an amenable semigroup and $\sigma$ is an involution of $G.$
In this paper we will investigate the solutions and stability of the generalized variant of Wilson's functional equation $$ (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 ternary modules over ternary algebras and using fixed point methods, we prove the stability and super-stability of ternary additive, quadratic, cubic and quartic derivations and $\sigma$-homomorphisms in such…
In this paper, we establish the conditional Hyers-Ulam-Rassias stability of the generalized Jensen functional equation $r f \left (\frac{sx+ty}{r}) = s g(x) + t h(y)$ on various restricted domains such as inside balls, outside balls, and…
Let $S$ be a semigroup and $X$ a Banach space. The functional equation $\phi (xyz)+ \phi (x) + \phi (y) + \phi (z) = \phi (xy) + \phi (yz) + \phi (xz)$ is said to be stable for the pair $(X, S)$ if and only if $f: S\to X$ satisfying $\|…
In this paper, we introduce the concept of j-hom-derivation, $j\in\{1,2\}$ and solve the new generalized additive-quadratic functional equations in the sense of ternary Banach algebras. Moreover, using the fixed point method, we prove its…
In this paper we prove that the so--called entropy equation, i.e., \[ H\left(x, y, z\right)=H\left(x+y, 0, z\right)+H\left(x, y, 0\right) \] is stable in the sense of Hyers and Ulam on the positive cone of $\mathbb{R}^{3}$, assuming that…