# On the Stability of Quadratic Functional Equations

## Related Articles

- Approximate Behavior of Bi-Quadratic Mappings in Quasinormed Spaces. Won-Gil Park; Jae-Hyeong Bae // Journal of Inequalities & Applications;2010, Vol. 2010, p1
We obtain the generalized Hyers-Ulam stability of the bi-quadratic functional equation f(x+y, z+ w) + f(x + y, z - w) + f(x - y, z + w) + f(x - y, z - w) = 4[f(x, z) + f(x,w) + f(y, z) + (y,w)] in quasinormed spaces.

- Hyers-Ulam-Rassias Stability of Orthogonal Quadratic Functional Equation. Kumar, Manoj; Chugh, Renu // International Journal of Computer Applications;2013, Vol. 62, p42
In this paper, we study the Hyers-Ulam-Rassias stability of the quadratic functional equations f(3xÂ±y)=f(xÂ±y)+16f(x) for the mapping f from orthogonal linear space in to Banach space. Furthermore, we establish the asymptotic behavior of the above quadratic functional equation. The main...

- On the Stability of Generalized Quartic Mappings in Quasi-Î²-Normed Spaces. Dongseung Kang // Journal of Inequalities & Applications;2010, Vol. 2010, p1
We investigate the generalized Hyers-Ulam-Rassias stability problem in quasi-Î²-normed spaces and then the stability by using a subadditive function for the generalized quartic function f : X â†’ Y such that f(ax+by)+f(ax-by)-2a2(a2 -b2)f(x) = (ab)2[f(x+y)+f(x-y)]-2b2(a2 -b2)f(y), where...

- On the hyperstability of a Cauchy-Jensen type functional equation in Banach spaces. EL-Fassi, Iz-iddine; Kabbaj, Samir // Proyecciones - Journal of Mathematics;Dec2015, Vol. 34 Issue 4, p359
In this paper, we establish some hyperstability results of the following Cauchy-Jensen functional equation f ( x + y/ 2 + z) + f ( x - y/ 2 + z) = f (x) + 2f (z) in Banach spaces.

- On the Generalized Hyers-Ulam Stability of the Generalized Polynomial Function of Degree 3. Yang-Hi Lee // Tamsui Oxford Journal of Mathematical Sciences (TOJMS);2008, Vol. 24 Issue 4, p429
his paper the generalized Hyers-Ulam stability is proved for the following functional equation 4âˆ‘i=0 4 Ci(- 1)4-i f(ix + y) = 0 following the spirit of the approach that was introduced in the paper of Th.M. Rassias, On, the stability of the linear mapping in Banach spaces, Proc. Amer....

- On bi-Cubic functional equations. Fazeli, A.; Amini Sarteshnizi, E. // Journal of Computational Analysis & Applications;Dec2013, Vol. 15 Issue 8, p1413
In this paper, we investigate the solution and Hyers-Ulam stability of the following bi-cubic functional equation f(2x + y, 2z + w) + f(2x -y,2z- w) = 2f(x + y, z + w) + 2f(x -y,z-w) + 12f(x, z) in Banach spaces.

- INNER PRODUCT SPACES AND FUNCTIONAL EQUATIONS. // Journal of Computational Analysis & Applications;Jan2011, Vol. 13 Issue 1, p296
No abstract available.

- Cauchyâ€“Rassias Stability of Cauchyâ€“Jensen Additive Mappings in Banach Spaces. Baak, Choonkil // Acta Mathematica Sinica;Oct2006, Vol. 22 Issue 6, p1789
Let X, Y be vector spaces. It is shown that if a mapping f : X â†’ Y satisfies (0.1) (0.2) or (0.3) for all x, y, z âˆˆ X, then the mapping f : X â†’ Y is Cauchy additive. Furthermore, we prove the Cauchyâ€“Rassias stability of the functional equations (0.1), (0.2) and (0.3) in...

- Generalized Hyers-Ulam stability of a general mixed additive-cubic functional equation in quasi-Banach spaces. Xu, Tian; Rassias, John; Xu, Wan // Acta Mathematica Sinica;Mar2012, Vol. 28 Issue 3, p529
In this paper, we establish a general solution and the generalized Hyers-Ulam-Rassias stability of the following general mixed additive-cubic functional equation in the quasi-Banach spaces.