## Abstract and Applied Analysis

### Fixed Points and Stability of an Additive Functional Equation of $n$-Apollonius Type in $C^{*}$-Algebras

#### Abstract

Using the fixed point method, we prove the generalized Hyers-Ulam stability of ${C}^{\ast}$-algebra homomorphisms and of generalized derivations on ${C}^{\ast}$-algebras for the following functional equation of Apollonius type ${\sum }_{i=1}^{n}f(z-{x}_{i})=-(1/n){\sum }_{1\leq i< j\leq n}f({x}_{i}+{x}_{j})+nf(z-(1/{n}^{2}){\sum }_{i=1}^{n}{x}_{i})$.

#### Article information

Source
Abstr. Appl. Anal., Volume 2008 (2008), Article ID 672618, 13 pages.

Dates
First available in Project Euclid: 10 February 2009

https://projecteuclid.org/euclid.aaa/1234298988

Digital Object Identifier
doi:10.1155/2008/672618

Mathematical Reviews number (MathSciNet)
MR2439255

Zentralblatt MATH identifier
1159.47032

#### Citation

Moradlou, Fridoun; Vaezi, Hamid; Park, Choonkil. Fixed Points and Stability of an Additive Functional Equation of $n$ -Apollonius Type in $C^{*}$ -Algebras. Abstr. Appl. Anal. 2008 (2008), Article ID 672618, 13 pages. doi:10.1155/2008/672618. https://projecteuclid.org/euclid.aaa/1234298988

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