## Abstract and Applied Analysis

### Jordan ${\ast}$-Derivations on ${C}^{\ast}$-Algebras and $J{C}^{\ast}$-Algebras

#### Abstract

We investigate Jordan ${\ast}$-derivations on ${C}^{\ast}$-algebras and Jordan ${\ast}$-derivations on $J{C}^{\ast}$-algebras associated with the following functional inequality $\Vert f(x)+f(y)+kf(z)\Vert \leq \Vert kf((x+y)/k+z)\Vert$ for some integer $k$ greater than 1. We moreover prove the generalized Hyers-Ulam stability of Jordan ${\ast}$-derivations on ${C}^{\ast}$-algebras and of Jordan ${\ast}$-derivations on $JC^{\ast}$-algebras associated with the following functional equation $f((x+y)/k+z) = (f(x)+f(y))/k+f(z)$ for some integer $k$ greater than 1.

#### Article information

Source
Abstr. Appl. Anal., Volume 2008 (2008), Article ID 410437, 12 pages.

Dates
First available in Project Euclid: 10 February 2009

https://projecteuclid.org/euclid.aaa/1234299003

Digital Object Identifier
doi:10.1155/2008/410437

Mathematical Reviews number (MathSciNet)
MR2471252

Zentralblatt MATH identifier
1243.46046

#### Citation

Su An, Jong; Cui, Jianlian; Park, Choonkil. Jordan ${\ast}$ -Derivations on ${C}^{\ast}$ -Algebras and $J{C}^{\ast}$ -Algebras. Abstr. Appl. Anal. 2008 (2008), Article ID 410437, 12 pages. doi:10.1155/2008/410437. https://projecteuclid.org/euclid.aaa/1234299003

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