Kil-Woung Jun

The generalized Hyers–Ulam–Rassias stability of a cubic functional equation☆

Abstract In this paper, we obtain the general solution and the generalized Hyers–Ulam stability for a cubic functional equation f(2x+y)+f(2x−y)=2f(x+y)+2f(x−y)+12f(x) .

ON THE STABILITY OF APPROXIMATELY ADDITIVE MAPPINGS

In this paper we prove a generalization of the stability of approximately additive mappings in the spirit of Hyers, Ulam and Rassias.

EXTENDED HYERS-ULAM STABILITY FOR A CAUCHY-JENSEN MAPPINGS

In 1940, Ulam proposed the famous Ulam stability problem. In 1941, Hyers solved the well-known Ulam stability problem for additive mappings subject to the Hyers condition on approximately additive mappings. In 2003–2006, the last author of this paper investigated the Hyers–Ulam stability of additive and Jensen type mappings. In this paper, we improve results obtained in 2003 and 2005 for Jensen type mappings and establish new theorems about the Ulam stability of additive and alternative additive mappings. These stability results can be applied in stochastic analysis, financial and actuarial mathematics, as well as in psychology and sociology.

ON THE HYERS-ULAM STABILITY OF A GENERALIZED QUADRATIC AND ADDITIVE FUNCTIONAL EQUATION

In this paper, we obtain the general solution of a gen-eralized quadratic and additive type functional equation f(x + ay) + af(x - y) = f(x - ay) + af(x + y) for any integer a with a -1. 0, 1 in the class of functions between real vector spaces and investigate the generalized Hyers- Ulam stability problem for the equation.

HYERS-ULAM-RASSIAS STABILITY OF A QUADRATIC TYPE FUNCTIONAL EQUATION

In this paper, we prove the stability of a quadratic type functional equation a 2 f x + y + z a + a 2 f x i y + z a + a 2 f x + y i z a + a 2 f ix + y + z a = 4f(x) + 4f(y) + 4f(z):

ON DERIVATIONS IN BANACH ALGEBRAS

Our main goal is to show that if there exist Jordan derivations D and G on a noncommutative (n + 1)!-torsion free prime ring R such that D(x)x n i x n G(x) 2 C(R) for all x 2 R, then we have D = 0 and G = 0. We also prove that if there exists a derivation D on a noncommutative 2-torsion free prime ring R such that the mapping x 7! (aD(x);x) is commuting on R, then we have either a = 0 or D = 0.

A GENERALIZATION OF THE HYERS-ULAM-RASSIAS STABILITY OF A FUNCTIONAL EQUATION OF DAVISON

We prove the Hyers-Ulam-Rassias stability of the Dav- ison functional equation f(xy) + f(x + y) = f(xy + x) + f(y) for a class of functions from a ring into a Banach space and we also investigate the Davison equation of Pexider type.

On the Hyers-Ulam-Rassias Stability of a Pexiderized Quadratic Equation II

In this paper we prove a generalization of the stability of the Pexiderized quadratic equations f 1(x + y + z) + f 2(x) + f 3(y) + f 4(z) − f 5(x + y) − f 6(y + z) − f 7(x + z) = 0 and f 1(x + y + z) + f 2(x-y + z) + f 3(x + y − z) + f 4(− x + y + z) − 4f 5(x) − 4f 6(y) − 4f 7(z) = 0 in the spirit of D.H. Hyers, S.M. Ulam, Th.M. Rassias and P. Gǎvruta.

On the Hyers-Ulam-Rassias Stability of the Bi-Jensen Functional Equation

In this paper, we obtain the Hyers–Ulam–Rassias stability of a bi-Pexider functional equation