## Abstract and Applied Analysis

### Homomorphisms and Derivations in ${C}^{\ast}$-Ternary Algebras

#### Abstract

In 2006, C. Park proved the stability of homomorphisms in ${C}^{\ast\,\!}$-ternary algebras and of derivations on ${C}^{\ast\,\!}$-ternary algebras for the following generalized Cauchy-Jensen additive mapping: $2f(({\sum}_{j=1}^{p}{x}_{j}/2)+{\sum }_{j=1}^{d}{y}_{j})={\sum}_{j=1}^{p}f({x}_{j})+2{\sum }_{j=1}^{d}f({y}_{j})$. In this note, we improve and generalize some results concerning this functional equation.

#### Article information

Source
Abstr. Appl. Anal., Volume 2009 (2009), Article ID 612392, 16 pages.

Dates
First available in Project Euclid: 16 March 2010

https://projecteuclid.org/euclid.aaa/1268745559

Digital Object Identifier
doi:10.1155/2009/612392

Mathematical Reviews number (MathSciNet)
MR2516001

Zentralblatt MATH identifier
1169.39304

#### Citation

Najati, Abbas; Park, Choonkil; Lee, Jung Rye. Homomorphisms and Derivations in ${C}^{\ast}$ -Ternary Algebras. Abstr. Appl. Anal. 2009 (2009), Article ID 612392, 16 pages. doi:10.1155/2009/612392. https://projecteuclid.org/euclid.aaa/1268745559

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