Related papers: Stability of quadratic functional equation in modu…
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 work, we prove the generalised Hyer Ulam stability of the following functional equation \begin{equation}\label{Eq-1} \phi(x)+\phi(y)+\phi(z)=q \phi\left(\sqrt[s]{\frac{x^s+y^s+z^s}{q}}\right),\qquad |q| \leq 1 \end{equation} and $s$…
By adopting the direct method and fixed point method, we prove that the Hyers-Ulam stability of the following additive-quadratic functional equation \begin{equation} f(x+y, z+w)+f(x-y, z-w)-2 f(x, z)-2 f(x, w)=0 \end{equation} in…
In this paper, we investigate some hyperstability results, inspired by the concept of Ulam stability, for the following functional equations: \begin{equation} \varphi(x+y)+\varphi(x-y)=2\varphi(x)+2\varphi(y) \end{equation} \begin{equation}…
In this paper we investigate the generalized Hyers- Ulam stability of the functional equation $$f (2x +y)+f (2x -y)= f (x + y)+ f (x -y)+2f (2x)-2f (x)$$ in fuzzy Banach spaces.
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…
In this paper, we establish the general solution of the functional equation $$f(nx+y)+f(nx-y)=n^2f(x+y)+n^2f(x-y)+2(f(nx)-n^2f(x))-2(n^2-1)f(y)\eqno {0 cm}$$for fixed integers $n$ with $n\neq0,\pm1$ and investigate the generalized…
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…
In this paper, we achieve the general solution and the generalized Hyers-Ulam-Rassias stability of the following functional equation $$f(x+ky)+f(x-ky)=k^2f(x+y)+k^2f(x-y)+2(1-k^2)f(x)\eqno {2 cm}$$for fixed integers $k$ with $k\neq0,\pm1$…
In this paper, we investigate the generalized Hyers-Ulam stability of the following reciprocal functional equation \begin{equation*}f(2x+y)+f\left(\frac{x+y}{2}\right)…
In this paper, we obtain the general solution of the following functional equation f(3x + y + z) + f(x + 3y + z) + f(x + y + 3z) + f(x) + f(y) + f(z) = 6f(x + y + z): We establish the Hyers-Ulam-Rassias stability of the above functional…
In this paper, we obtain the general solution and the generalized Ulam-Hyers stability of the cubic and quartic functional equation &4(f(3x+y)+f(3x-y))=-12(f(x+y)+f(x-y)) &+12(f(2x+y)+f(2x-y))-8f(y)-192f(x)+f(2y)+30f(2x).
We investigate the stability of Pexiderized mappings in Banach modules over a unital Banach algebra. As a consequence, we establish the Hyers--Ulam stability of the orthogonal Cauchy functional equation of Pexider type…
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 prove generalized Hyres-Ulam-Rassias stability of the cubic functional equation $f(kx+y)+f(kx-y)=k[f(x+y)+f(x-y)]+2(k^3-k)f(x)$ for all $k\in \Bbb N$ and the quartic functional equation…
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…
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.
In this paper, we obtain the general solution and the generalized Hyers-Ulam Rassias stability of the functional equation $$3(f(x+2y)+f(x-2y))=12(f(x+y)+f(x-y))+4f(3y)-18f(2y)+36f(y)-18f(x).$$
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 paper, we prove generalized Hyres--Ulam--Rassias stability of the mixed type additive, quadratic and cubic functional equation $$f(x+ky)+f(x-ky)=k^2f(x+y)+k^2f(x-y)+2(1-k^2)f(x)$$ for fixed integers $k$ with $k\neq0,\pm1$ in…