### Abstract

Let X, Y be Banach modules over a C*-algebra and let r, s be positive real numbers. We prove the stability of the following functional equation in Banach modules over a unital C*- algebra: rf (s(x - y)) + sf (r(y - x)) + (r + s)f (rx + sy) = (r + s) (rf(x) + sf(y)) . (0.1) We show that if r = s and an odd mapping f : X → Y satisfies the functional equation (0.1) then the odd mapping f : X → Y is Cauchy additive. As an application, we show that every almost linear bijection h : A → B of a unital C*-algebra A onto a unital C*-algebra B is a C*-algebra isomorphism when h((2r)^{d}uy) = h((2r)^{d}u)h(y) for all unitaries u ∈ A, all y ∈ A, and all d ∈ Z.

Original language | English |
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Pages (from-to) | 112-125 |

Number of pages | 14 |

Journal | International Journal of Applied Mathematics and Statistics |

Volume | 7 |

Issue number | FO7 |

State | Published - 2007 Feb 1 |

### Keywords

- Euler-Lagrange type additive mapping
- Hyers-Ulam stability
- Isomorphism between C*-algebras

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## Cite this

Park, C. G., & Rassias, J. M. (2007). Hyers-ulam stability of an euler-lagrange type additive mapping.

*International Journal of Applied Mathematics and Statistics*,*7*(FO7), 112-125.