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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 Euler–Lagrange type cubic mappings in quasi-Banach spaces

Abstract In this paper, we solve the generalized Hyers–Ulam–Rassias stability problem for Euler–Lagrange type cubic functional equations f ( a x + y ) + f ( x + a y ) = ( a + 1 ) ( a − 1 ) 2 [ f ( x… Expand

Generalized Hyers–Ulam stability for general additive functional equations in quasi-β-normed spaces☆

- J. Rassias, H. Kim
- Mathematics
- 1 August 2009

Abstract In 1940 S.M. Ulam proposed the famous Ulam stability problem. In 1941 D.H. Hyers solved the well-known Ulam stability problem for additive mappings subject to the Hyers condition on… Expand

On the stability problem for a mixed type of quartic and quadratic functional equation

- H. Kim
- Mathematics
- 1 December 2006

Let E1 and E2 be real linear spaces. In this paper, we determine the general solution for a mixed type functional equation of a quartic and a quadratic mapping f:E1→E2,
… Expand

On the stability of an n-dimensional quadratic and additive functional equation

In this paper, we investigate the generalized Hyers-Ulam stability problem of a quadratic and additive type functional equation f ( n ∑ i=1 xi ) + (n − 2) n ∑ i=1 f (xi) = ∑ 1 i<j n f (xi + xj), (n >… Expand

On the Hyers-Ulam-Rassias stability of a general cubic functional equation

In this paper, we solve the generalized Hyers-Ulam-Rassias stability problem for a cubic functional equation f (x + 2y) + f (x− 2y) + 6f (x) = 4f (x + y) + 4f (x− y) in the spirit of Hyers, Ulam,… Expand

Superhard tantalum-nitride films formed by inductively coupled plasma-assisted sputtering

- Gyu-Ho Lee, H. Kim, Hyunwoo Choi, J. Lee
- Materials Science
- 26 February 2007

Abstract The effect of inductively coupled plasma (ICP) power on the mechanical properties of tantalum-nitride films was investigated. TaN films were grown on an Si (001) substrate using ICP assisted… Expand

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… Expand

REMARKS ON THE STABILITY OF ADDITIVE FUNCTIONAL EQUATION

In this paper, using an idea from the direct method of Hyers, we give the conditions in order for a linear mapping near an approximately additive mapping to exist.

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